33:"/_next/static/immutable/chunks/2bq63k8dyqm9u.js" 34:"/_next/static/immutable/chunks/0_ity8j5ejt48.js" 35:"/_next/static/immutable/chunks/2qrlq-55dy_32.js" 36:"/_next/static/immutable/chunks/06pfjhybvbklo.js" 37:I[88154,["$1","$2","$3","$4","$33","$34","$35","$36"],"CardViewEvent"] 38:"DefinitionPageStatement" 39:I[16068,["$1","$2","$3","$4","$33","$34","$35","$36"],"$38"] 3e:I[27201,["$1","$2","$3","$4"],"IconMark"] 3a:T4c5,[[DEF-SYMBOL-401|$=$|ref]] [[DEF-SYMBOL-402|$\ne$|ref]] [[DEF-SYMBOL-423|$\equiv$|ref]] [[DEF-SYMBOL-424|$\propto$|ref]] [[DEF-SYMBOL-420|$\sim$|ref]] [[DEF-SYMBOL-428|$\simeq$|ref]] [[DEF-SYMBOL-421|$\cong$|ref]] [[DEF-SYMBOL-422|$\approx$|ref]] [[DEF-SYMBOL-403|$<$|ref]] [[DEF-SYMBOL-404|$\le\,\leqq$|ref]] [[DEF-SYMBOL-405|$>$|ref]] [[DEF-SYMBOL-406|$\ge\,\geqq$|ref]] [[DEF-SYMBOL-407|$\in$|ref]] [[DEF-SYMBOL-408|$\notin$|ref]] [[DEF-SYMBOL-409|$\ni$|ref]] [[DEF-SYMBOL-410|$\not\ni$|ref]] [[DEF-SYMBOL-411|$\subseteq\,\subseteqq$|ref]] [[DEF-SYMBOL-412|$\not\subseteq\,\not\subseteqq$|ref]] [[DEF-SYMBOL-413|$\subset\,\subsetneq\,\subsetneqq$|ref]] [[DEF-SYMBOL-414|$\not\subset\,\not\subsetneq\,\not\subsetneqq$|ref]] [[DEF-SYMBOL-415|$\supseteq\,\supseteqq$|ref]] [[DEF-SYMBOL-416|$\not\supseteq\,\not\supseteqq$|ref]] [[DEF-SYMBOL-417|$\supset\,\supsetneq\,\supsetneqq$|ref]] [[DEF-SYMBOL-418|$\not\supset\,\not\supsetneq\,\not\supsetneqq$|ref]] [[DEF-SYMBOL-425|$\parallel$|ref]] [[DEF-SYMBOL-426|$\perp$|ref]] [[DEF-SYMBOL-419|$\vdash$|ref]] [[DEF-SYMBOL-427|$\models$|ref]] [[DEF-SYMBOL-803|$\mapsto$|ref]] [[DEF-SYMBOL-804|$\longmapsto$|ref]]3b:T54d,[[DEF-ALP-001|$A$|ref]] [[DEF-ALP-002|$B$|ref]] [[DEF-ALP-003|$C$|ref]] [[DEF-ALP-004|$D$|ref]] [[DEF-ALP-005|$E$|ref]] [[DEF-ALP-006|$F$|ref]] [[DEF-ALP-007|$G$|ref]] [[DEF-ALP-008|$H$|ref]] [[DEF-ALP-009|$I$|ref]] [[DEF-ALP-010|$J$|ref]] [[DEF-ALP-011|$K$|ref]] [[DEF-ALP-012|$L$|ref]] [[DEF-ALP-013|$M$|ref]] [[DEF-ALP-014|$N$|ref]] [[DEF-ALP-015|$O$|ref]] [[DEF-ALP-016|$P$|ref]] [[DEF-ALP-017|$Q$|ref]] [[DEF-ALP-018|$R$|ref]] [[DEF-ALP-019|$S$|ref]] [[DEF-ALP-020|$T$|ref]] [[DEF-ALP-021|$U$|ref]] [[DEF-ALP-022|$V$|ref]] [[DEF-ALP-023|$W$|ref]] [[DEF-ALP-024|$X$|ref]] [[DEF-ALP-025|$Y$|ref]] [[DEF-ALP-026|$Z$|ref]] [[DEF-ALP-027|$a$|ref]] [[DEF-ALP-028|$b$|ref]] [[DEF-ALP-029|$c$|ref]] [[DEF-ALP-030|$d$|ref]] [[DEF-ALP-031|$e$|ref]] [[DEF-ALP-032|$f$|ref]] [[DEF-ALP-033|$g$|ref]] [[DEF-ALP-034|$h$|ref]] [[DEF-ALP-035|$i$|ref]] [[DEF-ALP-036|$j$|ref]] [[DEF-ALP-037|$k$|ref]] [[DEF-ALP-038|$l$|ref]] [[DEF-ALP-039|$m$|ref]] [[DEF-ALP-040|$n$|ref]] [[DEF-ALP-041|$o$|ref]] [[DEF-ALP-042|$p$|ref]] [[DEF-ALP-043|$q$|ref]] [[DEF-ALP-044|$r$|ref]] [[DEF-ALP-045|$s$|ref]] [[DEF-ALP-046|$t$|ref]] [[DEF-ALP-047|$u$|ref]] [[DEF-ALP-048|$v$|ref]] [[DEF-ALP-049|$w$|ref]] [[DEF-ALP-050|$x$|ref]] [[DEF-ALP-051|$y$|ref]] [[DEF-ALP-052|$z$|ref]]3c:T789,[[DEF-FRK-001|$\mathfrak{A}$|ref]] [[DEF-FRK-002|$\mathfrak{B}$|ref]] [[DEF-FRK-003|$\mathfrak{C}$|ref]] 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[[DEF-FRK-032|$\mathfrak{f}$|ref]] [[DEF-FRK-033|$\mathfrak{g}$|ref]] [[DEF-FRK-034|$\mathfrak{h}$|ref]] [[DEF-FRK-035|$\mathfrak{i}$|ref]] [[DEF-FRK-036|$\mathfrak{j}$|ref]] [[DEF-FRK-037|$\mathfrak{k}$|ref]] [[DEF-FRK-038|$\mathfrak{l}$|ref]] [[DEF-FRK-039|$\mathfrak{m}$|ref]] [[DEF-FRK-040|$\mathfrak{n}$|ref]] [[DEF-FRK-041|$\mathfrak{o}$|ref]] [[DEF-FRK-042|$\mathfrak{p}$|ref]] [[DEF-FRK-043|$\mathfrak{q}$|ref]] [[DEF-FRK-044|$\mathfrak{r}$|ref]] [[DEF-FRK-045|$\mathfrak{s}$|ref]] [[DEF-FRK-046|$\mathfrak{t}$|ref]] [[DEF-FRK-047|$\mathfrak{u}$|ref]] [[DEF-FRK-048|$\mathfrak{v}$|ref]] [[DEF-FRK-049|$\mathfrak{w}$|ref]] [[DEF-FRK-050|$\mathfrak{x}$|ref]] [[DEF-FRK-051|$\mathfrak{y}$|ref]] [[DEF-FRK-052|$\mathfrak{z}$|ref]]3d:T5b7,[[DEF-GRK-001|$A$|ref]] [[DEF-GRK-002|$B$|ref]] [[DEF-GRK-003|$\Gamma$|ref]] [[DEF-GRK-004|$\Delta$|ref]] [[DEF-GRK-005|$E$|ref]] [[DEF-GRK-006|$Z$|ref]] [[DEF-GRK-007|$H$|ref]] [[DEF-GRK-008|$\Theta$|ref]] [[DEF-GRK-009|$I$|ref]] [[DEF-GRK-010|$K$|ref]] [[DEF-GRK-011|$\Lambda$|ref]] [[DEF-GRK-012|$M$|ref]] [[DEF-GRK-013|$N$|ref]] [[DEF-GRK-014|$\Xi$|ref]] [[DEF-GRK-015|$O$|ref]] [[DEF-GRK-016|$\Pi$|ref]] [[DEF-GRK-017|$P$|ref]] [[DEF-GRK-018|$\Sigma$|ref]] [[DEF-GRK-019|$T$|ref]] [[DEF-GRK-020|$\Upsilon$|ref]] [[DEF-GRK-021|$\Phi$|ref]] [[DEF-GRK-022|$X$|ref]] [[DEF-GRK-023|$\Psi$|ref]] [[DEF-GRK-024|$\Omega$|ref]] [[DEF-GRK-025|$\alpha$|ref]] [[DEF-GRK-026|$\beta$|ref]] [[DEF-GRK-027|$\gamma$|ref]] [[DEF-GRK-028|$\delta$|ref]] [[DEF-GRK-029|$\epsilon\,\varepsilon$|ref]] [[DEF-GRK-030|$\zeta$|ref]] [[DEF-GRK-031|$\eta$|ref]] [[DEF-GRK-032|$\theta\,\vartheta$|ref]] [[DEF-GRK-033|$\iota$|ref]] [[DEF-GRK-034|$\kappa\,\varkappa$|ref]] [[DEF-GRK-035|$\lambda$|ref]] [[DEF-GRK-036|$\mu$|ref]] [[DEF-GRK-037|$\nu$|ref]] [[DEF-GRK-038|$\xi$|ref]] [[DEF-GRK-039|$o$|ref]] [[DEF-GRK-040|$\pi\,\varpi$|ref]] [[DEF-GRK-041|$\rho\,\varrho$|ref]] [[DEF-GRK-042|$\sigma\,\varsigma$|ref]] [[DEF-GRK-043|$\tau$|ref]] [[DEF-GRK-044|$\upsilon$|ref]] 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\$a,b,c,d\$ に対して、\$(a+b)(c+d)=ac+ad+bc+bd\$ が成り立つ。","logical_statement_md":"\\[\n\\forall a,b,c,d\\in\\mathbb{R},\\ (a+b)(c+d)=ac+ad+bc+bd\n\\]","conditions_md":"\$a,b,c,d\$ は実数。","notation_md":"\$(a+b)(c+d)\$ は \$a+b\$ と \$c+d\$ の積を表す。","free_example_md":null},{"id":"prop-abs-010","topic_id":"topic-analysis","subtopic":"absolute-value","subtopic_title":"絶対値","subsubtopic":null,"subsubtopic_title":null,"code":"ABS-010","slug":"absolute-value-nonnegative","title":"絶対値の非負性","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"任意の実数 \$a\$ に対して、\$|a|\\ge 0\$ である。","logical_statement_md":"\\[\n\\forall a\\in\\mathbb{R},\\ |a|\\ge0\n\\]","conditions_md":"\$a\$ は実数。","notation_md":"\$|a|\$ は \$a\$ の絶対値。","free_example_md":null},{"id":"prop-exp-010","topic_id":"topic-algebra","subtopic":"expansion-formulas","subtopic_title":"展開公式","subsubtopic":null,"subsubtopic_title":null,"code":"EXP-010","slug":"square-of-sum-expansion","title":"和の平方の展開公式","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"任意の実数 \$a,b\$ に対して、\$(a+b)^2=a^2+2ab+b^2\$ が成り立つ。","logical_statement_md":"\\[\n\\forall a,b\\in\\mathbb{R},\\ (a+b)^2=a^2+2ab+b^2\n\\]","conditions_md":"\$a,b\$ は実数。","notation_md":"\$(a+b)^2\$ は \$a+b\$ と \$a+b\$ の積を表す。","free_example_md":null},{"id":"prop-real-010","topic_id":"topic-algebra","subtopic":"expansion-formulas","subtopic_title":"展開公式","subsubtopic":null,"subsubtopic_title":null,"code":"REAL-010","slug":"subtract-expanded-sum","title":"かっこのマイナス展開","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"実数の和からかっこ付きの和を引くとき、かっこの中の各項の符号を反転して展開できる。","logical_statement_md":"\\[\n\\forall p,q,r,s,t,u\\in\\mathbb{R},\\ p+q+r-(s+t+u)=p+q+r-s-t-u\n\\]","conditions_md":"\$p,q,r,s,t,u\$ は実数。","notation_md":"\$-(s+t+u)\$ は、かっこの中の各項の符号を反転して加えることを表す。","free_example_md":null},{"id":"prop-ineq-010","topic_id":"topic-analysis","subtopic":"inequalities","subtopic_title":"不等式","subsubtopic":null,"subsubtopic_title":null,"code":"INEQ-010","slug":"triangle-inequality-real","title":"三角不等式","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"任意の実数 \$a,b\$ に対して、\$|a+b| \\le |a|+|b|\$ が成り立つ。","logical_statement_md":"\\[\n\\forall a,b\\in\\mathbb{R},\\ |a+b|\\le |a|+|b|\n\\]","conditions_md":"\$a,b\$ は実数。","notation_md":"\$|a+b|\$ は和 \$a+b\$ の絶対値。","free_example_md":null},{"id":"prop-abs-020","topic_id":"topic-analysis","subtopic":"absolute-value","subtopic_title":"絶対値","subsubtopic":null,"subsubtopic_title":null,"code":"ABS-020","slug":"absolute-value-square","title":"絶対値の平方","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":20,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"任意の実数 \$a\$ に対して、\$|a|^2=a^2\$ である。","logical_statement_md":"\\[\n\\forall a\\in\\mathbb{R},\\ |a|^2=a^2\n\\]","conditions_md":"\$a\$ は実数。","notation_md":"\$|a|^2\$ は絶対値を取ってから平方すること。","free_example_md":null},{"id":"prop-real-020","topic_id":"topic-analysis","subtopic":"real-order","subtopic_title":"実数の順序","subsubtopic":null,"subsubtopic_title":null,"code":"REAL-020","slug":"real-positive-product","title":"正の数の積","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":20,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"実数 \$x,y\$ について、\$x>0\$ かつ \$y>0\$ ならば \$xy>0\$ である。","logical_statement_md":"\\[\nx,y\\in\\mathbb{R}\\land x>0\\land y>0 \\Rightarrow xy>0\n\\]","conditions_md":"\$x,y\$ は実数。\$x>0\$, \$y>0\$。","notation_md":"\$xy\$ は \$x\$ と \$y\$ 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の絶対値。","free_example_md":null},{"id":"prop-abs-030","topic_id":"topic-analysis","subtopic":"absolute-value","subtopic_title":"絶対値","subsubtopic":null,"subsubtopic_title":null,"code":"ABS-030","slug":"absolute-value-product","title":"積の絶対値","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":30,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"任意の実数 \$a,b\$ に対して、\$|ab|=|a||b|\$ である。","logical_statement_md":"\\[\n\\forall a,b\\in\\mathbb{R},\\ |ab|=|a||b|\n\\]","conditions_md":"\$a,b\$ は実数。","notation_md":"\$ab\$ は \$a\$ と \$b\$ の積。","free_example_md":null},{"id":"prop-real-030","topic_id":"topic-analysis","subtopic":"real-order","subtopic_title":"実数の順序","subsubtopic":null,"subsubtopic_title":null,"code":"REAL-030","slug":"square-comparison-nonnegative","title":"非負な数の平方比較","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":30,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"\$A\\ge 0\$, \$B\\ge 0\$ のとき、\$A\\le B\$ は \$A^2\\le B^2\$ と同値である。","logical_statement_md":"\\[\nA,B\\in\\mathbb{R}_{\\ge0}\\Rightarrow (A\\le B\\Leftrightarrow A^2\\le B^2)\n\\]","conditions_md":"\$A,B\$ は非負の実数。","notation_md":"\$A^2\$ は \$A\$ の平方。","free_example_md":null},{"id":"prop-abs-040","topic_id":"topic-analysis","subtopic":"absolute-value","subtopic_title":"絶対値","subsubtopic":null,"subsubtopic_title":null,"code":"ABS-040","slug":"absolute-value-dominates-value","title":"絶対値は元以上","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":40,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"任意の実数 \$x\$ に対して、\$|x|\\ge x\$ である。","logical_statement_md":"\\[\n\\forall x\\in\\mathbb{R},\\ |x|\\ge x\n\\]","conditions_md":"\$x\$ は実数。","notation_md":"\$|x|\$ は \$x\$ の絶対値。","free_example_md":null},{"id":"prop-real-040","topic_id":"topic-analysis","subtopic":"real-order","subtopic_title":"実数の順序","subsubtopic":null,"subsubtopic_title":null,"code":"REAL-040","slug":"square-difference-comparison-nonnegative","title":"非負数の平方差比較","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":40,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","statement_md":"\$A\\ge0\$, \$B\\ge0\$ で、\$B^2-A^2\\ge0\$ ならば、\$A\\le B\$ である。","logical_statement_md":"\\[\nA,B\\in\\mathbb{R}_{\\ge0}\\land B^2-A^2\\ge0\\Rightarrow A\\le B\n\\]","conditions_md":"\$A,B\$ は非負の実数。","notation_md":"\$B^2-A^2\$ は平方した後の差。","free_example_md":null}],"definitions":[{"id":"def-def-tana-000","topic_id":"topic-tana-words","subtopic":null,"subtopic_title":null,"subsubtopic":null,"subsubtopic_title":null,"code":"DEF-TANA-000","slug":"symbol-term","title":"記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":0,"created_at":"2026-06-29T06:42:02.756Z","updated_at":"2026-06-29T06:42:02.756Z","body_md":"この教材では、使ってよいと決める文字を **記号** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false},{"id":"def-def-alp-000","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-000","slug":"alphabet","title":"アルファベット","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":0,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"$3b","detail_md":null,"logical_statement_md":"\\[\n\\begin{array}{ccccccccccccc}\nA&B&C&D&E&F&G&H&I&J&K&L&M\\\\\nN&O&P&Q&R&S&T&U&V&W&X&Y&Z\\\\\na&b&c&d&e&f&g&h&i&j&k&l&m\\\\\nn&o&p&q&r&s&t&u&v&w&x&y&z\n\\end{array}\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-000","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-000","slug":"bold-alphabet","title":"黒板太字アルファベット","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":0,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-BLD-001|\$\\mathbb{A}\$|ref]] [[DEF-BLD-002|\$\\mathbb{B}\$|ref]] [[DEF-BLD-003|\$\\mathbb{C}\$|ref]] [[DEF-BLD-004|\$\\mathbb{D}\$|ref]] [[DEF-BLD-005|\$\\mathbb{E}\$|ref]] [[DEF-BLD-006|\$\\mathbb{F}\$|ref]] [[DEF-BLD-007|\$\\mathbb{G}\$|ref]] [[DEF-BLD-008|\$\\mathbb{H}\$|ref]] [[DEF-BLD-009|\$\\mathbb{I}\$|ref]] [[DEF-BLD-010|\$\\mathbb{J}\$|ref]] [[DEF-BLD-011|\$\\mathbb{K}\$|ref]] [[DEF-BLD-012|\$\\mathbb{L}\$|ref]] [[DEF-BLD-013|\$\\mathbb{M}\$|ref]] \n\n[[DEF-BLD-014|\$\\mathbb{N}\$|ref]] [[DEF-BLD-015|\$\\mathbb{O}\$|ref]] [[DEF-BLD-016|\$\\mathbb{P}\$|ref]] [[DEF-BLD-017|\$\\mathbb{Q}\$|ref]] [[DEF-BLD-018|\$\\mathbb{R}\$|ref]] [[DEF-BLD-019|\$\\mathbb{S}\$|ref]] [[DEF-BLD-020|\$\\mathbb{T}\$|ref]] [[DEF-BLD-021|\$\\mathbb{U}\$|ref]] [[DEF-BLD-022|\$\\mathbb{V}\$|ref]] [[DEF-BLD-023|\$\\mathbb{W}\$|ref]] [[DEF-BLD-024|\$\\mathbb{X}\$|ref]] [[DEF-BLD-025|\$\\mathbb{Y}\$|ref]] [[DEF-BLD-026|\$\\mathbb{Z}\$|ref]]","detail_md":null,"logical_statement_md":"\\[\n\\begin{array}{ccccccccccccc}\n\\mathbb{A}&\\mathbb{B}&\\mathbb{C}&\\mathbb{D}&\\mathbb{E}&\\mathbb{F}&\\mathbb{G}&\\mathbb{H}&\\mathbb{I}&\\mathbb{J}&\\mathbb{K}&\\mathbb{L}&\\mathbb{M}\\\\\n\\mathbb{N}&\\mathbb{O}&\\mathbb{P}&\\mathbb{Q}&\\mathbb{R}&\\mathbb{S}&\\mathbb{T}&\\mathbb{U}&\\mathbb{V}&\\mathbb{W}&\\mathbb{X}&\\mathbb{Y}&\\mathbb{Z}\n\\end{array}\n\\]","notation_md":null,"listed":true},{"id":"def-def-cal-000","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-000","slug":"calligraphic-alphabet","title":"カリグラフィ体アルファベット","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":0,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-CAL-001|\$\\mathcal{A}\$|ref]] [[DEF-CAL-002|\$\\mathcal{B}\$|ref]] [[DEF-CAL-003|\$\\mathcal{C}\$|ref]] [[DEF-CAL-004|\$\\mathcal{D}\$|ref]] [[DEF-CAL-005|\$\\mathcal{E}\$|ref]] [[DEF-CAL-006|\$\\mathcal{F}\$|ref]] [[DEF-CAL-007|\$\\mathcal{G}\$|ref]] [[DEF-CAL-008|\$\\mathcal{H}\$|ref]] [[DEF-CAL-009|\$\\mathcal{I}\$|ref]] [[DEF-CAL-010|\$\\mathcal{J}\$|ref]] [[DEF-CAL-011|\$\\mathcal{K}\$|ref]] [[DEF-CAL-012|\$\\mathcal{L}\$|ref]] [[DEF-CAL-013|\$\\mathcal{M}\$|ref]] \n\n[[DEF-CAL-014|\$\\mathcal{N}\$|ref]] [[DEF-CAL-015|\$\\mathcal{O}\$|ref]] [[DEF-CAL-016|\$\\mathcal{P}\$|ref]] [[DEF-CAL-017|\$\\mathcal{Q}\$|ref]] [[DEF-CAL-018|\$\\mathcal{R}\$|ref]] [[DEF-CAL-019|\$\\mathcal{S}\$|ref]] [[DEF-CAL-020|\$\\mathcal{T}\$|ref]] [[DEF-CAL-021|\$\\mathcal{U}\$|ref]] [[DEF-CAL-022|\$\\mathcal{V}\$|ref]] [[DEF-CAL-023|\$\\mathcal{W}\$|ref]] [[DEF-CAL-024|\$\\mathcal{X}\$|ref]] [[DEF-CAL-025|\$\\mathcal{Y}\$|ref]] [[DEF-CAL-026|\$\\mathcal{Z}\$|ref]]","detail_md":null,"logical_statement_md":"\\[\n\\begin{array}{ccccccccccccc}\n\\mathcal{A}&\\mathcal{B}&\\mathcal{C}&\\mathcal{D}&\\mathcal{E}&\\mathcal{F}&\\mathcal{G}&\\mathcal{H}&\\mathcal{I}&\\mathcal{J}&\\mathcal{K}&\\mathcal{L}&\\mathcal{M}\\\\\n\\mathcal{N}&\\mathcal{O}&\\mathcal{P}&\\mathcal{Q}&\\mathcal{R}&\\mathcal{S}&\\mathcal{T}&\\mathcal{U}&\\mathcal{V}&\\mathcal{W}&\\mathcal{X}&\\mathcal{Y}&\\mathcal{Z}\n\\end{array}\n\\]","notation_md":null,"listed":true},{"id":"def-def-frk-000","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-000","slug":"fraktur","title":"フラクトゥール体アルファベット","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":0,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"$3c","detail_md":null,"logical_statement_md":"\\[\n\\begin{array}{ccccccccccccc}\n\\mathfrak{A}&\\mathfrak{B}&\\mathfrak{C}&\\mathfrak{D}&\\mathfrak{E}&\\mathfrak{F}&\\mathfrak{G}&\\mathfrak{H}&\\mathfrak{I}&\\mathfrak{J}&\\mathfrak{K}&\\mathfrak{L}&\\mathfrak{M}\\\\\n\\mathfrak{N}&\\mathfrak{O}&\\mathfrak{P}&\\mathfrak{Q}&\\mathfrak{R}&\\mathfrak{S}&\\mathfrak{T}&\\mathfrak{U}&\\mathfrak{V}&\\mathfrak{W}&\\mathfrak{X}&\\mathfrak{Y}&\\mathfrak{Z}\\\\\n\\mathfrak{a}&\\mathfrak{b}&\\mathfrak{c}&\\mathfrak{d}&\\mathfrak{e}&\\mathfrak{f}&\\mathfrak{g}&\\mathfrak{h}&\\mathfrak{i}&\\mathfrak{j}&\\mathfrak{k}&\\mathfrak{l}&\\mathfrak{m}\\\\\n\\mathfrak{n}&\\mathfrak{o}&\\mathfrak{p}&\\mathfrak{q}&\\mathfrak{r}&\\mathfrak{s}&\\mathfrak{t}&\\mathfrak{u}&\\mathfrak{v}&\\mathfrak{w}&\\mathfrak{x}&\\mathfrak{y}&\\mathfrak{z}\n\\end{array}\n\\]","notation_md":null,"listed":true},{"id":"def-def-grk-000","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-000","slug":"greek-letters","title":"ギリシャ文字","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":0,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"$3d","detail_md":null,"logical_statement_md":"\\[\n\\begin{array}{cccccccccccc}\nA&B&\\Gamma&\\Delta&E&Z&H&\\Theta&I&K&\\Lambda&M\\\\\nN&\\Xi&O&\\Pi&P&\\Sigma&T&\\Upsilon&\\Phi&X&\\Psi&\\Omega\\\\\n\\alpha&\\beta&\\gamma&\\delta&\\epsilon\\,\\varepsilon&\\zeta&\\eta&\\theta\\,\\vartheta&\\iota&\\kappa\\,\\varkappa&\\lambda&\\mu\\\\\n\\nu&\\xi&o&\\pi\\,\\varpi&\\rho\\,\\varrho&\\sigma\\,\\varsigma&\\tau&\\upsilon&\\phi\\,\\varphi&\\chi&\\psi&\\omega\n\\end{array}\n\\]","notation_md":null,"listed":true},{"id":"def-def-pri-000","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-000","slug":"primitive-language-symbols","title":"原始言語の記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":0,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-401|\$=\$]] [[DEF-SYMBOL-407|\$\\in\$]] [[DEF-SYMBOL-303|\$\\neg\$]] [[DEF-SYMBOL-306|\$\\to\$]] [[DEF-SYMBOL-301|\$\\forall\$]] [[|\$v_1\$|text]] [[|\$v_2\$|text]] [[|\$v_3\$|text]] \$\\ldots\$ を **原始言語で用いる記号** とする。","detail_md":null,"logical_statement_md":"\\[\n=,\\ \\in,\\ \\neg,\\ \\to,\\ \\forall,\\ v_1,\\ v_2,\\ v_3,\\ldots\n\\]","notation_md":"続けて [[|\$v_4\$|text]] [[|\$v_5\$|text]] [[|\$v_6\$|text]] \$\\ldots\$ も原始言語で用いる[[|変数記号|link]]とする。","listed":true},{"id":"def-def-not-000","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-000","slug":"variable-symbol-occurrence-notation","title":"変数記号の出現記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":0,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"論理式 \$\\varphi\$ における変数記号の出現が \$v_1,v_2,\\ldots,v_k\$ であるとき、\$\\varphi\$ を [[|\$\\varphi(v_1,v_2,\\ldots,v_k)\$|text]] と書く。","detail_md":null,"logical_statement_md":"\\[\n\\varphi(v_1,v_2,\\ldots,v_k)\n\\]","notation_md":null,"listed":true},{"id":"def-def-dgt-000","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-000","slug":"digits","title":"数字","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":0,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[DEF-DGT-001|\$0\$|ref]] [[DEF-DGT-002|\$1\$|ref]] [[DEF-DGT-003|\$2\$|ref]] [[DEF-DGT-004|\$3\$|ref]] [[DEF-DGT-005|\$4\$|ref]] [[DEF-DGT-006|\$5\$|ref]] [[DEF-DGT-007|\$6\$|ref]] [[DEF-DGT-008|\$7\$|ref]] [[DEF-DGT-009|\$8\$|ref]] [[DEF-DGT-010|\$9\$|ref]]","detail_md":null,"logical_statement_md":"\\[\n0\\quad1\\quad2\\quad3\\quad4\\quad5\\quad6\\quad7\\quad8\\quad9\n\\]","notation_md":null,"listed":true},{"id":"def-def-tana-001","topic_id":"topic-tana-words","subtopic":null,"subtopic_title":null,"subsubtopic":null,"subsubtopic_title":null,"code":"DEF-TANA-001","slug":"mathematical-object","title":"対象","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-06-29T06:42:02.756Z","updated_at":"2026-06-29T06:42:02.756Z","body_md":"**対象** とは、この教材で扱う[[DEF-TANA-000|記号]]をまとめてよぶ言葉である。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false},{"id":"def-def-bld-001","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-001","slug":"bold-uppercase-a","title":"\$\\mathbb{A}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{A}\$|text]] を **黒板太字エー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{A}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-001","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-001","slug":"calligraphic-uppercase-a","title":"\$\\mathcal{A}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{A}\$|text]] を **カリグラフィエー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{A}\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-001","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-001","slug":"existential-symbol-notation","title":"存在の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-303,DEF-SYMBOL-301|\$\\neg\\,(\\,\\forall v_1\\,(\\neg\\,\\varphi)\\,)\$|ref]] を [[DEF-SYMBOL-302|\$\\exists v_1\\,\\varphi\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,\\exists v_1\\,\\varphi\\,)\\coloneqq(\\,\\neg\\,(\\,\\forall v_1\\,(\\neg\\,\\varphi)\\,)\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-frk-001","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-001","slug":"fraktur-uppercase-a","title":"\$\\mathfrak{A}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{A}\$|text]] を **フラクトゥール大文字エー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{A}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-001","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-001","slug":"greek-uppercase-alpha","title":"\$A\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$A\$|text]] を **大文字アルファ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nA\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-001","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-001","slug":"primitive-language-auxiliary-symbol","title":"原始言語の補助記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-902|\$\\,\\mathpunct{,}\\,\$]] [[DEF-SYMBOL-911|\$\\ldots\$]] [[DEF-SYMBOL-914|\$\\mathopen{(}\\ \\mathclose{)}\$]] を **原始言語で用いる補助記号** とする。","detail_md":null,"logical_statement_md":"\\[\n\\mathpunct{,}\\quad \\ldots\\quad \\mathopen{(}\\ \\mathclose{)}\n\\]","notation_md":"補助記号は読みやすさを補うために使う[[DEF-TANA-000|記号|link]]である。","listed":true},{"id":"def-def-alp-001","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-001","slug":"uppercase-a","title":"\$A\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$A\$|text]] を **アルファベット大文字エー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nA\n\\]","notation_md":null,"listed":false},{"id":"def-def-otl-001","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-001","slug":"aleph","title":"\$\\aleph\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\aleph\$|text]] を **アレフ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\aleph\n\\]","notation_md":null,"listed":false},{"id":"def-def-dgt-001","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-001","slug":"digit-zero","title":"\$0\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$0\$|text]] を **ゼロ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n0\n\\]","notation_md":null,"listed":false},{"id":"def-def-frm-001","topic_id":"topic-words-and-symbols","subtopic":"expressions","subtopic_title":"式","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRM-001","slug":"equality-formula","title":"等号式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":1,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[DEF-SYMBOL-401|\$v_i=v_j\$]] を **等号式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nv_i=v_j\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-002","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-002","slug":"bold-uppercase-b","title":"\$\\mathbb{B}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{B}\$|text]] を **黒板太字ビー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{B}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-002","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-002","slug":"calligraphic-uppercase-b","title":"\$\\mathcal{B}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{B}\$|text]] を **カリグラフィビー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{B}\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-002","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-002","slug":"disjunction-symbol-notation","title":"選言の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-303,DEF-SYMBOL-306|\$(\\,\\neg\\,\\varphi\\to\\psi\\,)\$|ref]] を [[DEF-SYMBOL-305|\$\\varphi\\lor\\psi\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,\\varphi\\lor\\psi\\,)\\coloneqq(\\,(\\neg\\,\\varphi)\\to\\psi\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-frk-002","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-002","slug":"fraktur-uppercase-b","title":"\$\\mathfrak{B}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{B}\$|text]] を **フラクトゥール大文字ビー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{B}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-002","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-002","slug":"greek-uppercase-beta","title":"\$B\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$B\$|text]] を **大文字ベータ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nB\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-002","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-002","slug":"primitive-language-atomic-formula","title":"原始言語の原子論理式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"\$i,j\$ をそれぞれ \$1,2,\\ldots\$ のいずれかとする。\n\n[[|変数記号|link]] \$\\,v_1,v_2,\\ldots\$ に対して、\n\n[[DEF-FRM-001|\$v_i=v_j\$|ref]] [[DEF-FRM-002|\$v_i\\in v_j\$|ref]] を **原始言語の原子論理式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nv_i=v_j,\\quad v_i\\in v_j\n\\]","notation_md":"[[DEF-FRM-001|\$v_1=v_1\$|ref]] [[DEF-FRM-001|\$v_1=v_2\$|ref]] [[DEF-FRM-001|\$v_1=v_3\$|ref]] \$\\,\\cdots\\,\$ [[DEF-FRM-001|\$v_2=v_1\$|ref]] [[DEF-FRM-001|\$v_2=v_2\$|ref]] \$\\,\\cdots\\,\$ [[DEF-FRM-001|\$v_3=v_1\$|ref]] \$\\,\\cdots\\,\$\n\n[[DEF-FRM-002|\$v_1\\in v_1\$|ref]] [[DEF-FRM-002|\$v_1\\in v_2\$|ref]] [[DEF-FRM-002|\$v_1\\in v_3\$|ref]] \$\\,\\cdots\\,\$ [[DEF-FRM-002|\$v_2\\in v_1\$|ref]] [[DEF-FRM-002|\$v_2\\in v_2\$|ref]] \$\\,\\cdots\\,\$\n[[DEF-FRM-002|\$v_3\\in v_1\$|ref]] \$\\,\\cdots\\,\$\n\nが **原始言語の原子論理式** である。","listed":true},{"id":"def-def-alp-002","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-002","slug":"uppercase-b","title":"\$B\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$B\$|text]] を **アルファベット大文字ビー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nB\n\\]","notation_md":null,"listed":false},{"id":"def-def-otl-002","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-002","slug":"beth","title":"\$\\beth\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\beth\$|text]] を **ベート** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\beth\n\\]","notation_md":null,"listed":false},{"id":"def-def-dgt-002","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-002","slug":"digit-one","title":"\$1\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$1\$|text]] を **イチ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n1\n\\]","notation_md":null,"listed":false},{"id":"def-def-frm-002","topic_id":"topic-words-and-symbols","subtopic":"expressions","subtopic_title":"式","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRM-002","slug":"membership-formula","title":"所属式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":2,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[DEF-SYMBOL-407|\$v_i\\in v_j\$]] を **所属式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nv_i\\in v_j\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-003","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-003","slug":"bold-uppercase-c","title":"\$\\mathbb{C}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{C}\$|text]] を **黒板太字シー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{C}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-003","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-003","slug":"calligraphic-uppercase-c","title":"\$\\mathcal{C}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{C}\$|text]] を **カリグラフィシー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{C}\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-003","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-003","slug":"conjunction-symbol-notation","title":"連言の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-303,DEF-SYMBOL-306|\$\\neg\\,(\\,\\varphi\\to\\neg\\,\\psi\\,)\$|ref]] を [[DEF-SYMBOL-304|\$\\varphi\\land\\psi\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,\\varphi\\land\\psi\\,)\\coloneqq(\\,\\neg\\,(\\,\\varphi\\to\\neg\\,\\psi\\,)\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-frk-003","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-003","slug":"fraktur-uppercase-c","title":"\$\\mathfrak{C}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{C}\$|text]] を **フラクトゥール大文字シー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{C}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-003","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-003","slug":"greek-uppercase-gamma","title":"\$\\Gamma\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\Gamma\$|text]] を **大文字ガンマ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Gamma\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-003","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-003","slug":"primitive-language-formula","title":"原始言語の論理式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"\$i\$ を \$1,2,\\ldots\$ のいずれかとする。\n\n[[DEF-PRI-002|**原子論理式**|link]] を **原始言語の論理式** とよぶ。\n\n[[|**変数記号**|link]] \$\\,v_1,v_2,\\ldots\$ と **原始言語の論理式** \$\\,\\varphi,\\psi\$ に対して、\n\n[[DEF-FRM-003|\$\\neg\\,\\varphi\$|ref]] [[DEF-FRM-004|\$\\varphi\\to\\psi\$|ref]] [[DEF-FRM-005|\$\\forall v_i\\,\\varphi\$|ref]] も **原始言語の論理式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nv_i=v_j,\\quad v_i\\in v_j,\\quad \\neg\\,\\varphi,\\quad \\varphi\\to\\psi,\\quad \\forall v_i\\,\\varphi\n\\]","notation_md":null,"listed":true},{"id":"def-def-alp-003","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-003","slug":"uppercase-c","title":"\$C\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$C\$|text]] を **アルファベット大文字シー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nC\n\\]","notation_md":null,"listed":false},{"id":"def-def-dgt-003","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-003","slug":"digit-two","title":"\$2\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$2\$|text]] を **ニ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n2\n\\]","notation_md":null,"listed":false},{"id":"def-def-otl-003","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-003","slug":"gimel","title":"\$\\gimel\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\gimel\$|text]] を **ギメル** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\gimel\n\\]","notation_md":null,"listed":false},{"id":"def-def-frm-003","topic_id":"topic-words-and-symbols","subtopic":"expressions","subtopic_title":"式","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRM-003","slug":"negation-formula","title":"否定式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":3,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[DEF-SYMBOL-303|\$\\neg\\,\\varphi\$]] を **否定式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\neg\\,\\varphi\n\\]","notation_md":null,"listed":true},{"id":"def-def-not-004","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-004","slug":"biconditional-symbol-notation","title":"同値の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-303,DEF-SYMBOL-306|\$\\neg\\,(\\,(\\,\\varphi\\to\\psi\\,)\\to\\neg\\,(\\,\\psi\\to\\varphi\\,)\\,)\$|ref]] を [[DEF-SYMBOL-308|\$\\varphi\\leftrightarrow\\psi\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,\\varphi\\leftrightarrow\\psi\\,)\\coloneqq(\\,\\neg\\,(\\,(\\,\\varphi\\to\\psi\\,)\\to\\neg\\,(\\,\\psi\\to\\varphi\\,)\\,)\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-004","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-004","slug":"bold-uppercase-d","title":"\$\\mathbb{D}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{D}\$|text]] を **黒板太字ディー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{D}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-004","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-004","slug":"calligraphic-uppercase-d","title":"\$\\mathcal{D}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{D}\$|text]] を **カリグラフィディー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{D}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-004","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-004","slug":"fraktur-uppercase-d","title":"\$\\mathfrak{D}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{D}\$|text]] を **フラクトゥール大文字ディー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{D}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-004","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-004","slug":"greek-uppercase-delta","title":"\$\\Delta\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\Delta\$|text]] を **大文字デルタ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Delta\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-004","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-004","slug":"uppercase-d","title":"\$D\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$D\$|text]] を **アルファベット大文字ディー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nD\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-004","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-004","slug":"variable-symbol-occurrence-in-atomic-formula","title":"原子論理式における変数記号の出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-PRI-002|**原始言語の原子論理式**|link]] [[DEF-PRI-002|\$v_i=v_j\$|ref]] に対して、\n\n[[|\$v_i=v_j\$|text]] の \$v_i\$ と \$v_j\$ のそれぞれを [[|\$v_i=v_j\$|text]] **における変数記号の出現** とよぶ。\n\n[[DEF-PRI-002|**原始言語の原子論理式**|link]] [[DEF-PRI-002|\$v_i\\in v_j\$|ref]] に対して、\n\n[[|\$v_i\\in v_j\$|text]] の \$v_i\$ と \$v_j\$ のそれぞれを [[|\$v_i\\in v_j\$|text]] **における変数記号の出現** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":"\$j=i\$ の場合も右側の \$v_i\$ と左側の \$v_i\$ を区別する。","listed":true},{"id":"def-def-otl-004","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-004","slug":"daleth","title":"\$\\daleth\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\daleth\$|text]] を **ダレット** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\daleth\n\\]","notation_md":null,"listed":false},{"id":"def-def-dgt-004","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-004","slug":"digit-three","title":"\$3\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$3\$|text]] を **サン** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n3\n\\]","notation_md":null,"listed":false},{"id":"def-def-frm-004","topic_id":"topic-words-and-symbols","subtopic":"expressions","subtopic_title":"式","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRM-004","slug":"implication-formula","title":"含意式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":4,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[DEF-SYMBOL-306|\$\\varphi\\to\\psi\$]] を **含意式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\varphi\\to\\psi\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-005","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-005","slug":"bold-uppercase-e","title":"\$\\mathbb{E}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{E}\$|text]] を **黒板太字イー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{E}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-005","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-005","slug":"calligraphic-uppercase-e","title":"\$\\mathcal{E}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{E}\$|text]] を **カリグラフィイー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{E}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-005","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-005","slug":"fraktur-uppercase-e","title":"\$\\mathfrak{E}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{E}\$|text]] を **フラクトゥール大文字イー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{E}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-005","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-005","slug":"greek-uppercase-epsilon","title":"\$E\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$E\$|text]] を **大文字イプシロン** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nE\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-005","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-005","slug":"not-equal-symbol-notation","title":"不等の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-303,DEF-SYMBOL-401|\$\\neg\\,(v_1=v_2)\$|ref]] を [[DEF-SYMBOL-402|\$v_1\\ne v_2\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,v_1\\ne v_2\\,)\\coloneqq(\\,\\neg\\,(v_1=v_2)\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-alp-005","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-005","slug":"uppercase-e","title":"\$E\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$E\$|text]] を **アルファベット大文字イー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nE\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-005","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-005","slug":"variable-symbol-occurrence-in-negation-formula","title":"否定論理式における変数記号の出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"\$\\varphi\$ を [[DEF-PRI-003|**原始言語の論理式**|link]] とする。\n\n[[DEF-PRI-003|**原始言語の否定論理式**|link]] [[DEF-PRI-003|\$\\neg\\,\\varphi\$|ref]] に対して、\n\n[[|\$\\neg\\,\\varphi\$|text]] **における変数記号の出現** を \$\\varphi\$ における変数記号の出現で定める。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-dgt-005","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-005","slug":"digit-four","title":"\$4\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$4\$|text]] を **ヨン** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n4\n\\]","notation_md":null,"listed":false},{"id":"def-def-otl-005","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-005","slug":"script-l","title":"\$\\ell\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\ell\$|text]] を **筆記体エル** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\ell\n\\]","notation_md":null,"listed":false},{"id":"def-def-frm-005","topic_id":"topic-words-and-symbols","subtopic":"expressions","subtopic_title":"式","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRM-005","slug":"universal-formula","title":"全称式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":5,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[DEF-SYMBOL-301|\$\\forall v_i\\,\\varphi\$]] を **全称式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\forall v_i\\,\\varphi\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-006","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-006","slug":"bold-uppercase-f","title":"\$\\mathbb{F}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{F}\$|text]] を **黒板太字エフ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{F}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-006","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-006","slug":"calligraphic-uppercase-f","title":"\$\\mathcal{F}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{F}\$|text]] を **カリグラフィエフ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{F}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-006","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-006","slug":"fraktur-uppercase-f","title":"\$\\mathfrak{F}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{F}\$|text]] を **フラクトゥール大文字エフ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{F}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-006","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-006","slug":"greek-uppercase-zeta","title":"\$Z\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$Z\$|text]] を **大文字ゼータ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nZ\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-006","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-006","slug":"not-membership-symbol-notation","title":"非所属の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-303,DEF-SYMBOL-407|\$\\neg\\,(v_1\\in v_2)\$|ref]] を [[DEF-SYMBOL-408|\$v_1\\notin v_2\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,v_1\\notin v_2\\,)\\coloneqq(\\,\\neg\\,(v_1\\in v_2)\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-alp-006","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-006","slug":"uppercase-f","title":"\$F\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$F\$|text]] を **アルファベット大文字エフ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nF\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-006","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-006","slug":"variable-symbol-occurrence-in-implication-formula","title":"含意論理式における変数記号の出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"\$\\varphi,\\psi\$ を [[DEF-PRI-003|**原始言語の論理式**|link]] とする。\n\n[[DEF-PRI-003|**原始言語の含意論理式**|link]] [[DEF-PRI-003|\$\\varphi\\to\\psi\$|ref]] に対して、\n\n[[|\$\\varphi\\to\\psi\$|text]] **における変数記号の出現** を \$\\varphi\$ における変数記号の出現と \$\\psi\$ における変数記号の出現で定める。\n\nただし、[[|\$\\varphi\\to\\psi\$|text]] **における変数記号の出現** において、\$\\varphi\$ における変数記号の出現と \$\\psi\$ における変数記号の出現は区別する。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-dgt-006","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-006","slug":"digit-five","title":"\$5\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$5\$|text]] を **ゴ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n5\n\\]","notation_md":null,"listed":false},{"id":"def-def-otl-006","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-006","slug":"dotless-i","title":"\$\\imath\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\imath\$|text]] を **点なしアイ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\imath\n\\]","notation_md":null,"listed":false},{"id":"def-def-frm-006","topic_id":"topic-words-and-symbols","subtopic":"expressions","subtopic_title":"式","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRM-006","slug":"negation-logical-formula","title":"否定論理式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":6,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$\\varphi\$ を **論理式** とするとき、[[DEF-FRM-003|\$\\neg\\,\\varphi\$]] を **否定論理式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\neg\\,\\varphi\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-007","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-007","slug":"bold-uppercase-g","title":"\$\\mathbb{G}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{G}\$|text]] を **黒板太字ジー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{G}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-007","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-007","slug":"calligraphic-uppercase-g","title":"\$\\mathcal{G}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{G}\$|text]] を **カリグラフィジー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{G}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-007","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-007","slug":"fraktur-uppercase-g","title":"\$\\mathfrak{G}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{G}\$|text]] を **フラクトゥール大文字ジー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{G}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-007","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-007","slug":"greek-uppercase-eta","title":"\$H\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$H\$|text]] を **大文字イータ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nH\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-007","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-007","slug":"reverse-membership-symbol-notation","title":"逆所属の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-407|\$v_1\\in v_2\$|ref]] を [[DEF-SYMBOL-409|\$v_2\\ni v_1\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,v_2\\ni v_1\\,)\\coloneqq (v_1\\in v_2)\n\\]","notation_md":null,"listed":true},{"id":"def-def-alp-007","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-007","slug":"uppercase-g","title":"\$G\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$G\$|text]] を **アルファベット大文字ジー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nG\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-007","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-007","slug":"variable-symbol-occurrence-in-universal-formula","title":"全称論理式における変数記号の出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"\$i\$ を \$1,2,\\ldots\$ のいずれかとする。\n\n\$v_1,v_2,\\ldots\$ を [[|**変数記号**|link]]、\$\\varphi\$ を [[DEF-PRI-003|**原始言語の論理式**|link]] とする。\n\n[[DEF-PRI-003|**原始言語の全称論理式**|link]] [[DEF-PRI-003|\$\\forall v_i\\,\\varphi\$|ref]] に対して、\n\n[[|\$\\forall v_i\\,\\varphi\$|text]] **における変数記号の出現** を [[DEF-SYMBOL-301|全称記号|link]]の直後の \$v_i\$ と \$\\varphi\$ における変数記号の出現で定める。\n\nただし、[[|\$\\forall v_i\\,\\varphi\$|text]] **における変数記号の出現** において、[[DEF-SYMBOL-301|全称記号|link]]の直後の \$v_i\$ と、\$\\varphi\$ における変数記号の出現における \$v_i\$ は区別する。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-dgt-007","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-007","slug":"digit-six","title":"\$6\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$6\$|text]] を **ロク** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n6\n\\]","notation_md":null,"listed":false},{"id":"def-def-otl-007","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-007","slug":"dotless-j","title":"\$\\jmath\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\jmath\$|text]] を **点なしジェー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\jmath\n\\]","notation_md":null,"listed":false},{"id":"def-def-frm-007","topic_id":"topic-words-and-symbols","subtopic":"expressions","subtopic_title":"式","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRM-007","slug":"implication-logical-formula","title":"含意論理式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":7,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$\\varphi,\\psi\$ を **論理式** とするとき、[[DEF-FRM-004|\$\\varphi\\to\\psi\$]] を **含意論理式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\varphi\\to\\psi\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-008","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-008","slug":"bold-uppercase-h","title":"\$\\mathbb{H}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{H}\$|text]] を **黒板太字エイチ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{H}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-008","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-008","slug":"calligraphic-uppercase-h","title":"\$\\mathcal{H}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{H}\$|text]] を **カリグラフィエイチ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{H}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-008","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-008","slug":"fraktur-uppercase-h","title":"\$\\mathfrak{H}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{H}\$|text]] を **フラクトゥール大文字エイチ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{H}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-008","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-008","slug":"greek-uppercase-theta","title":"\$\\Theta\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\Theta\$|text]] を **大文字シータ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Theta\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-008","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-008","slug":"proper-subset-symbol-notation","title":"真部分の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-411,DEF-NOT-003|\$(\\,v_1\\subseteq v_2\\,)\\land (\\,v_1\\ne v_2\\,)\$|ref]] を [[DEF-SYMBOL-413|\$v_1\\subsetneq v_2\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,v_1\\subsetneq v_2\\,)\\coloneqq(\\,(\\,v_1\\subseteq v_2\\,)\\land (\\,v_1\\ne v_2\\,)\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-alp-008","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-008","slug":"uppercase-h","title":"\$H\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$H\$|text]] を **アルファベット大文字エイチ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nH\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-008","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-008","slug":"variable-symbol-occurrence-in-formula","title":"論理式における変数記号の出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-PRI-004|原子論理式における変数記号の出現]]\n\n[[DEF-PRI-005|否定論理式における変数記号の出現]]\n\n[[DEF-PRI-006|含意論理式における変数記号の出現]]\n\n[[DEF-PRI-007|全称論理式における変数記号の出現]]\n\nを **原始言語の論理式における変数記号の出現** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-dgt-008","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-008","slug":"digit-seven","title":"\$7\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$7\$|text]] を **ナナ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n7\n\\]","notation_md":null,"listed":false},{"id":"def-def-otl-008","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-008","slug":"h-bar","title":"\$\\hbar\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\hbar\$|text]] を **エイチバー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\hbar\n\\]","notation_md":null,"listed":false},{"id":"def-def-frm-008","topic_id":"topic-words-and-symbols","subtopic":"expressions","subtopic_title":"式","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRM-008","slug":"universal-logical-formula","title":"全称論理式","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":8,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$i\$ を \$1,2,\\ldots\$ のいずれかとする。\n\n\$v_i\$ を **変数記号**、\$\\varphi\$ を **論理式** とするとき、[[DEF-FRM-005|\$\\forall v_i\\,\\varphi\$]] を **全称論理式** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\forall v_i\\,\\varphi\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-009","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-009","slug":"bold-uppercase-i","title":"\$\\mathbb{I}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":9,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{I}\$|text]] を **黒板太字アイ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{I}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-009","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-009","slug":"calligraphic-uppercase-i","title":"\$\\mathcal{I}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":9,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{I}\$|text]] を **カリグラフィアイ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{I}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-009","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-009","slug":"fraktur-uppercase-i","title":"\$\\mathfrak{I}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":9,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{I}\$|text]] を **フラクトゥール大文字アイ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{I}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-009","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-009","slug":"greek-uppercase-iota","title":"\$I\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":9,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$I\$|text]] を **大文字イオタ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nI\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-009","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-009","slug":"not-proper-subset-symbol-notation","title":"非真部分の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":9,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[DEF-SYMBOL-303,DEF-SYMBOL-413|\$\\neg\\,(\\,v_1\\subsetneq v_2\\,)\$|ref]] を [[DEF-SYMBOL-414|\$v_1\\not\\subseteq v_2\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,v_1\\not\\subset v_2\\,)\\coloneqq(\\,\\neg\\,(\\,v_1\\subset v_2\\,)\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-alp-009","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-009","slug":"uppercase-i","title":"\$I\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":9,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$I\$|text]] を **アルファベット大文字アイ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nI\n\\]","notation_md":null,"listed":false},{"id":"def-def-dgt-009","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-009","slug":"digit-eight","title":"\$8\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":9,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$8\$|text]] を **ハチ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n8\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-009","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-009","slug":"free-occurrence-in-atomic-formula","title":"原子論理式における自由な出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":9,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[DEF-PRI-002|**原始言語の原子論理式**|link]] [[DEF-PRI-002|\$v_i=v_j\$|ref]] に対して、\n\n[[|\$v_i=v_j\$|text]] における [[DEF-PRI-004|**変数記号の出現**|link]] を [[|\$v_i=v_j\$|text]] **における自由な出現** とよぶ。\n\n[[DEF-PRI-002|**原始言語の原子論理式**|link]] [[DEF-PRI-002|\$v_i\\in v_j\$|ref]] に対して、\n\n[[|\$v_i\\in v_j\$|text]] における [[DEF-PRI-004|**変数記号の出現**|link]] を [[|\$v_i\\in v_j\$|text]] **における自由な出現** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-otl-009","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-009","slug":"weierstrass-p","title":"\$\\wp\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":9,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\wp\$|text]] を **ワイエルシュトラスのピー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\wp\n\\]","notation_md":null,"listed":false},{"id":"def-def-abs-010","topic_id":"topic-analysis","subtopic":"absolute-value","subtopic_title":"絶対値","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ABS-010","slug":"absolute-value-definition","title":"絶対値","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-06-28T09:57:07.330Z","updated_at":"2026-06-28T09:57:07.330Z","body_md":"実数 \$x\$ に対して、絶対値 \$|x|\$ を次のように定める。\n\n\\[\n|x| =\n\\begin{cases}\nx & (x\\ge0)\\\\\n-x & (x<0)\n\\end{cases}\n\\]","detail_md":"絶対値は、実数 \$x\$ が数直線上で \$0\$ からどれだけ離れているかを表す量である。\n定義では、\$x\\ge0\$ のときはそのまま \$x\$ とし、\$x<0\$ のときは符号を反転して \$-x\$ とする。\n\nそのため、どの場合でも \$|x|\\ge0\$ になる。これは [[ABS-010|絶対値の非負性]] で命題として扱う。\n\nまた、絶対値は平方と相性がよく、\$|x|^2=x^2\$ が成り立つ。これは [[ABS-020|絶対値の平方]] で確認する。","logical_statement_md":"\\[\n|x|\\coloneqq\\begin{cases}x&(x\\ge0)\\\\-x&(x<0)\\end{cases}\n\\]","notation_md":"\$|x|\$ は実数 \$x\$ の絶対値。","listed":true},{"id":"def-def-set-010","topic_id":"topic-set-theory","subtopic":"basic-set-language","subtopic_title":"集合の基本語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-010","slug":"set-definition","title":"集合","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-07-01T22:27:48.350Z","updated_at":"2026-07-01T22:27:48.350Z","body_md":"[[|\$\\mathsf{ZFC}\\,\$公理系|text]] において [[|変数記号|text]] が表す [[DEF-TANA-001|対象]] を **集合** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false},{"id":"def-def-bld-010","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-010","slug":"bold-uppercase-j","title":"\$\\mathbb{J}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{J}\$|text]] を **黒板太字ジェー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{J}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-010","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-010","slug":"calligraphic-uppercase-j","title":"\$\\mathcal{J}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{J}\$|text]] を **カリグラフィジェー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{J}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-010","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-010","slug":"fraktur-uppercase-j","title":"\$\\mathfrak{J}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{J}\$|text]] を **フラクトゥール大文字ジェー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{J}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-010","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-010","slug":"greek-uppercase-kappa","title":"\$K\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$K\$|text]] を **大文字カッパ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nK\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-010","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-010","slug":"uppercase-j","title":"\$J\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$J\$|text]] を **アルファベット大文字ジェー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nJ\n\\]","notation_md":null,"listed":false},{"id":"def-def-dgt-010","topic_id":"topic-words-and-symbols","subtopic":"digits","subtopic_title":"数字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-DGT-010","slug":"digit-nine","title":"\$9\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$9\$|text]] を **キュウ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n9\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-010","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-010","slug":"free-occurrence-in-negation-formula","title":"否定論理式における自由な出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$\\varphi\$ を [[DEF-PRI-003|**原始言語の論理式**|link]] とする。\n\n[[DEF-PRI-003|**原始言語の否定論理式**|link]] [[DEF-PRI-003|\$\\neg\\,\\varphi\$|ref]] に対して、\n\n[[|\$\\neg\\,\\varphi\$|text]] **における自由な出現** を \$\\varphi\$ における自由な出現で定める。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-otl-010","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-010","slug":"real-part-symbol","title":"\$\\Re\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":10,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\Re\$|text]] を **実部記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Re\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-011","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-011","slug":"not-subset-symbol-notation","title":"非部分の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":11,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[DEF-SYMBOL-303,DEF-SYMBOL-411|\$\\neg\\,(\\,v_1\\subseteq v_2\\,)\$|ref]] を [[DEF-SYMBOL-412|\$v_1\\not\\subseteq v_2\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(\\,v_1\\not\\subseteq v_2\\,)\\coloneqq(\\,\\neg\\,(v_1\\subseteq v_2)\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-011","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-011","slug":"bold-uppercase-k","title":"\$\\mathbb{K}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":11,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{K}\$|text]] を **黒板太字ケー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{K}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-011","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-011","slug":"calligraphic-uppercase-k","title":"\$\\mathcal{K}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":11,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{K}\$|text]] を **カリグラフィケー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{K}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-011","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-011","slug":"fraktur-uppercase-k","title":"\$\\mathfrak{K}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":11,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{K}\$|text]] を **フラクトゥール大文字ケー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{K}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-011","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-011","slug":"greek-uppercase-lambda","title":"\$\\Lambda\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":11,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\Lambda\$|text]] を **大文字ラムダ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Lambda\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-011","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-011","slug":"uppercase-k","title":"\$K\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":11,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$K\$|text]] を **アルファベット大文字ケー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nK\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-011","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-011","slug":"free-occurrence-in-implication-formula","title":"含意論理式における自由な出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":11,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$\\varphi,\\psi\$ を [[DEF-PRI-003|**原始言語の論理式**|link]] とする。\n\n[[DEF-PRI-003|**原始言語の含意論理式**|link]] [[DEF-PRI-003|\$\\varphi\\to\\psi\$|ref]] に対して、\n\n[[|\$\\varphi\\to\\psi\$|text]] **における自由な出現** を \$\\varphi\$ における自由な出現と \$\\psi\$ における自由な出現で定める。\n\nただし、[[|\$\\varphi\\to\\psi\$|text]] **における自由な出現** において、\$\\varphi\$ における自由な出現と \$\\psi\$ における自由な出現は区別する。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-otl-011","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-OTL-011","slug":"imaginary-part-symbol","title":"\$\\Im\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":11,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\Im\$|text]] を **虚部記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Im\n\\]","notation_md":null,"listed":false},{"id":"def-def-not-012","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-012","slug":"subset-notation","title":"部分の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":12,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[DEF-SYMBOL-301,DEF-SYMBOL-407,DEF-SYMBOL-306|\$\\forall v_3\\,(\\,(v_3\\in v_1)\\to (v_3\\in v_2)\\,)\$|ref]] を [[DEF-SYMBOL-411|\$v_1\\subseteq v_2\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n(v_1\\subseteq v_2)\\coloneqq(\\,\\forall v_3\\,(\\,(v_3\\in v_1)\\to (v_3\\in v_2)\\,)\\,)\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-012","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-012","slug":"bold-uppercase-l","title":"\$\\mathbb{L}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":12,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{L}\$|text]] を **黒板太字エル** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{L}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-012","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-012","slug":"calligraphic-uppercase-l","title":"\$\\mathcal{L}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":12,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{L}\$|text]] を **カリグラフィエル** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{L}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-012","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-012","slug":"fraktur-uppercase-l","title":"\$\\mathfrak{L}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":12,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{L}\$|text]] を **フラクトゥール大文字エル** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{L}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-012","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-012","slug":"greek-uppercase-mu","title":"\$M\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":12,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$M\$|text]] を **大文字ミュー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nM\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-012","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-012","slug":"uppercase-l","title":"\$L\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":12,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$L\$|text]] を **アルファベット大文字エル** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nL\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-012","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-012","slug":"free-occurrence-in-universal-formula","title":"全称論理式における自由な出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":12,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$i\$ を \$1,2,\\ldots\$ のいずれかとする。\n\n\$v_1,v_2,\\ldots\$ を [[|**変数記号**|link]]、\$\\varphi\$ を [[DEF-PRI-003|**原始言語の論理式**|link]] とする。\n\n[[DEF-PRI-003|**原始言語の全称論理式**|link]] [[DEF-PRI-003|\$\\forall v_i\\,\\varphi\$|ref]] に対して、\n\n[[|\$\\forall v_i\\,\\varphi\$|text]] **における自由な出現** を \$\\varphi\$ における自由な出現のうち \$v_i\$ でないもので定める。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-not-013","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-013","slug":"pairing-sentence-pair-notation","title":"対の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":13,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[DEF-NOT-004,DEF-NOT-002|\$\\forall v_1\\,\\forall v_2\\,\\exists v_3\\,\\forall v_4\\,\\left(\\,(v_4\\in v_3)\\leftrightarrow\\left(\\,(v_4=v_1)\\lor (v_4=v_2)\\,\\right)\\,\\right)\$|ref]] の \$v_3\$ を [[DEF-SYMBOL-916|\$\\{\\,v_1,v_2\\,\\}\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n\\{\\,v_1,v_2\\,\\}\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-013","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-013","slug":"bold-uppercase-m","title":"\$\\mathbb{M}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":13,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{M}\$|text]] を **黒板太字エム** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{M}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-013","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-013","slug":"calligraphic-uppercase-m","title":"\$\\mathcal{M}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":13,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{M}\$|text]] を **カリグラフィエム** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{M}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-013","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-013","slug":"fraktur-uppercase-m","title":"\$\\mathfrak{M}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":13,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{M}\$|text]] を **フラクトゥール大文字エム** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{M}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-013","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-013","slug":"greek-uppercase-nu","title":"\$N\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":13,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$N\$|text]] を **大文字ニュー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nN\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-013","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-013","slug":"uppercase-m","title":"\$M\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":13,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$M\$|text]] を **アルファベット大文字エム** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nM\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-013","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-013","slug":"free-occurrence-in-formula","title":"論理式における自由な出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":13,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[DEF-PRI-009|原子論理式における自由な出現]]\n\n[[DEF-PRI-010|否定論理式における自由な出現]]\n\n[[DEF-PRI-011|含意論理式における自由な出現]]\n\n[[DEF-PRI-012|全称論理式における自由な出現]]\n\nを **原始言語の論理式における自由な出現** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-not-014","topic_id":"topic-first-order-logic","subtopic":"abbreviated-notation","subtopic_title":"省略記法","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-NOT-014","slug":"single-notation","title":"単の記法","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":14,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[DEF-NOT-004|\$\\forall v_1\\,\\exists v_2\\,\\forall v_3\\,\\left(\\,(v_3\\in v_2)\\leftrightarrow (v_3=v_1)\\,\\right)\$|ref]] の \$v_2\$ を [[DEF-SYMBOL-916|\$\\{\\,v_1\\,\\}\$|ref]] と書く。","detail_md":null,"logical_statement_md":"\\[\n\\{\\,v_1\\,\\}\n\\]","notation_md":null,"listed":true},{"id":"def-def-bld-014","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-014","slug":"bold-uppercase-n","title":"\$\\mathbb{N}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":14,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{N}\$|text]] を **黒板太字エヌ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{N}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-014","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-014","slug":"calligraphic-uppercase-n","title":"\$\\mathcal{N}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":14,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{N}\$|text]] を **カリグラフィエヌ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{N}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-014","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-014","slug":"fraktur-uppercase-n","title":"\$\\mathfrak{N}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":14,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{N}\$|text]] を **フラクトゥール大文字エヌ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{N}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-014","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-014","slug":"greek-uppercase-xi","title":"\$\\Xi\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":14,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\Xi\$|text]] を **大文字クサイ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Xi\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-014","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-014","slug":"uppercase-n","title":"\$N\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":14,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$N\$|text]] を **アルファベット大文字エヌ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nN\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-014","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-014","slug":"free-variable-symbol-in-formula","title":"論理式における自由変数記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":14,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$i\$ を \$1,2,\\ldots\$ のいずれかとする。\n\n\$v_1,v_2,\\ldots\$ を [[|変数記号|link]]、\$\\varphi\$ を [[DEF-PRI-003|原始言語の論理式|link]] とする。\n\n\$\\varphi\$ [[DEF-PRI-008|における変数記号の出現|link]] のうちに \$v_i\$ の [[DEF-PRI-013|自由な出現|link]] があるとき、\$v_i\$ を \$\\varphi\$ における **自由変数記号** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-bld-015","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-015","slug":"bold-uppercase-o","title":"\$\\mathbb{O}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":15,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{O}\$|text]] を **黒板太字オー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{O}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-015","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-015","slug":"calligraphic-uppercase-o","title":"\$\\mathcal{O}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":15,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{O}\$|text]] を **カリグラフィオー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{O}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-015","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-015","slug":"fraktur-uppercase-o","title":"\$\\mathfrak{O}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":15,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{O}\$|text]] を **フラクトゥール大文字オー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{O}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-015","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-015","slug":"greek-uppercase-omicron","title":"\$O\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":15,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$O\$|text]] を **大文字オミクロン** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nO\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-015","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-015","slug":"uppercase-o","title":"\$O\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":15,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$O\$|text]] を **アルファベット大文字オー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nO\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-015","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-015","slug":"bound-occurrence-in-formula","title":"論理式における束縛された出現","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":15,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$i\$ を \$1,2,\\ldots\$ のいずれかとする。\n\n\$v_1,v_2,\\ldots\$ を [[|変数記号|link]]、\$\\varphi\$ を [[DEF-PRI-003|原始言語の論理式|link]] とする。\n\n\$\\varphi\$ [[DEF-PRI-008|における変数記号の出現|link]] のうち、[[DEF-PRI-013|自由な出現|link]] でないものを \$\\varphi\$ における **束縛された出現** とよぶ。\n\n\$v_i\$ が \$\\varphi\$ における **束縛された出現** であるとき、\$v_i\$ は \$\\varphi\$ において **束縛される** という。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-bld-016","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-016","slug":"bold-uppercase-p","title":"\$\\mathbb{P}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":16,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{P}\$|text]] を **黒板太字ピー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{P}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-016","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-016","slug":"calligraphic-uppercase-p","title":"\$\\mathcal{P}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":16,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{P}\$|text]] を **カリグラフィピー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{P}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-016","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-016","slug":"fraktur-uppercase-p","title":"\$\\mathfrak{P}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":16,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{P}\$|text]] を **フラクトゥール大文字ピー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{P}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-016","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-016","slug":"greek-uppercase-pi","title":"\$\\Pi\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":16,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\Pi\$|text]] を **大文字パイ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Pi\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-016","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-016","slug":"uppercase-p","title":"\$P\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":16,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$P\$|text]] を **アルファベット大文字ピー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nP\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-016","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-016","slug":"bound-variable-symbol-in-formula","title":"論理式における束縛変数記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":16,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$i\$ を \$1,2,\\ldots\$ のいずれかとする。\n\n\$v_1,v_2,\\ldots\$ を [[|変数記号|link]]、\$\\varphi\$ を [[DEF-PRI-003|原始言語の論理式|link]] とする。\n\n\$\\varphi\$ [[DEF-PRI-008|における変数記号の出現|link]] のうちに \$v_i\$ の [[DEF-PRI-015|束縛された出現|link]] があるとき、\$v_i\$ を \$\\varphi\$ における **束縛変数記号** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-bld-017","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-017","slug":"bold-uppercase-q","title":"\$\\mathbb{Q}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":17,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{Q}\$|text]] を **黒板太字キュー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{Q}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-017","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-017","slug":"calligraphic-uppercase-q","title":"\$\\mathcal{Q}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":17,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{Q}\$|text]] を **カリグラフィキュー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{Q}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-017","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-017","slug":"fraktur-uppercase-q","title":"\$\\mathfrak{Q}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":17,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{Q}\$|text]] を **フラクトゥール大文字キュー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{Q}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-017","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-017","slug":"greek-uppercase-rho","title":"\$P\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":17,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$P\$|text]] を **大文字ロー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nP\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-017","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-017","slug":"uppercase-q","title":"\$Q\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":17,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$Q\$|text]] を **アルファベット大文字キュー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nQ\n\\]","notation_md":null,"listed":false},{"id":"def-def-bld-018","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-018","slug":"bold-uppercase-r","title":"\$\\mathbb{R}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":18,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{R}\$|text]] を **黒板太字アール** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{R}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-018","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-018","slug":"calligraphic-uppercase-r","title":"\$\\mathcal{R}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":18,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{R}\$|text]] を **カリグラフィアール** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{R}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-018","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-018","slug":"fraktur-uppercase-r","title":"\$\\mathfrak{R}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":18,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{R}\$|text]] を **フラクトゥール大文字アール** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{R}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-018","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-018","slug":"greek-uppercase-sigma","title":"\$\\Sigma\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":18,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\Sigma\$|text]] を **大文字シグマ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Sigma\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-018","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-018","slug":"uppercase-r","title":"\$R\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":18,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$R\$|text]] を **アルファベット大文字アール** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nR\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-018","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-018","slug":"substitution-in-formula","title":"論理式における代入","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":18,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$i,j\$ を \$1,2,\\ldots\$ のいずれかとする。\n\n\$v_1,v_2,\\ldots\$ を [[DEF-PRI-000|変数記号|link]]、\$\\varphi\$ を [[DEF-PRI-003|原始言語の論理式|link]] とする。\n\n\$\\varphi\$ [[DEF-PRI-013|における自由な出現|link]] \$v_i\$ をすべて \$v_j\$ に書きかえることを\n\n\$\\varphi\$ **において \$v_i\$ に \$v_j\$ を代入する** という。\n\nこのとき、書きかえられた [[DEF-PRI-003|原始言語の論理式|link]] を \$\\varphi\$ において \$v_i\$ に \$v_j\$ を **代入した結果** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-bld-019","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-019","slug":"bold-uppercase-s","title":"\$\\mathbb{S}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":19,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{S}\$|text]] を **黒板太字エス** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{S}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-019","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-019","slug":"calligraphic-uppercase-s","title":"\$\\mathcal{S}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":19,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{S}\$|text]] を **カリグラフィエス** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{S}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-019","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-019","slug":"fraktur-uppercase-s","title":"\$\\mathfrak{S}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":19,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{S}\$|text]] を **フラクトゥール大文字エス** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{S}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-019","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-019","slug":"greek-uppercase-tau","title":"\$T\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":19,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$T\$|text]] を **大文字タウ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nT\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-019","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-019","slug":"uppercase-s","title":"\$S\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":19,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$S\$|text]] を **アルファベット大文字エス** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nS\n\\]","notation_md":null,"listed":false},{"id":"def-def-pri-019","topic_id":"topic-first-order-logic","subtopic":"primitive-language","subtopic_title":"原始言語","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-PRI-019","slug":"substitutability-in-formula","title":"論理式における代入可能性","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":19,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"\$i,j\$ を \$1,2,\\ldots\$ のいずれかとする。\n\n\$v_1,v_2,\\ldots\$ を [[DEF-PRI-000|変数記号|link]]、\$\\varphi\$ を [[DEF-PRI-003|原始言語の論理式|link]] とする。\n\n\$\\varphi\$ において \$v_i\$ に \$v_j\$ を [[DEF-PRI-018|代入した結果|link]] を \$\\psi\$ とする。\n\n\$\\varphi\$ [[DEF-PRI-013|における自由な出現|link]] \$v_i\$ を書きかえてできた \$v_j\$ がすべて、\$\\psi\$ [[DEF-PRI-013|における自由な出現|link]] であるとき、\$v_j\$ は \$\\varphi\$ において \$v_i\$ に **代入可能** であるという。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-bld-020","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-BLD-020","slug":"bold-uppercase-t","title":"\$\\mathbb{T}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":20,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathbb{T}\$|text]] を **黒板太字ティー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathbb{T}\n\\]","notation_md":null,"listed":false},{"id":"def-def-cal-020","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-CAL-020","slug":"calligraphic-uppercase-t","title":"\$\\mathcal{T}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":20,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathcal{T}\$|text]] を **カリグラフィティー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal{T}\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-020","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-020","slug":"fraktur-uppercase-t","title":"\$\\mathfrak{T}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":20,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{T}\$|text]] を **フラクトゥール大文字ティー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{T}\n\\]","notation_md":null,"listed":false},{"id":"def-def-grk-020","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-GRK-020","slug":"greek-uppercase-upsilon","title":"\$\\Upsilon\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":20,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\Upsilon\$|text]] を **大文字ウプシロン** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\Upsilon\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-020","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-020","slug":"uppercase-t","title":"\$T\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":20,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$T\$|text]] を **アルファベット大文字ティー** 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とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{x}\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-050","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-050","slug":"lowercase-x","title":"\$x\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":50,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$x\$|text]] を **アルファベット小文字エックス** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nx\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-051","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-051","slug":"fraktur-lowercase-y","title":"\$\\mathfrak{y}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":51,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{y}\$|text]] を **フラクトゥール小文字ワイ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{y}\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-051","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-051","slug":"lowercase-y","title":"\$y\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":51,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$y\$|text]] を **アルファベット小文字ワイ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\ny\n\\]","notation_md":null,"listed":false},{"id":"def-def-frk-052","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-FRK-052","slug":"fraktur-lowercase-z","title":"\$\\mathfrak{z}\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":52,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$\\mathfrak{z}\$|text]] を **フラクトゥール小文字ゼット** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathfrak{z}\n\\]","notation_md":null,"listed":false},{"id":"def-def-alp-052","topic_id":"topic-words-and-symbols","subtopic":"letters","subtopic_title":"文字","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-ALP-052","slug":"lowercase-z","title":"\$z\$","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":52,"created_at":"2026-07-13T22:15:25.846Z","updated_at":"2026-07-13T22:15:25.846Z","body_md":"[[|\$z\$|text]] を **アルファベット小文字ゼット** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nz\n\\]","notation_md":null,"listed":false},{"id":"def-def-set-062","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-062","slug":"binary-relation","title":"二項関係","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":62,"created_at":"2026-07-05T12:02:19.968Z","updated_at":"2026-07-05T12:02:19.968Z","body_md":"\$R\$ が [[DEF-SET-030|\$X\\times Y\$]] の [[|部分集合|text]] であるとき、[[DEF-SET-130|組 \$\\,(\\,X,Y,R\\,)\$]] を \$X\$ から \$Y\$ への **二項関係** とよぶ。","detail_md":null,"logical_statement_md":"\\[\nR\\subset X\\times Y\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-063","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-063","slug":"relation-source-definition","title":"始域","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":63,"created_at":"2026-07-05T12:02:19.968Z","updated_at":"2026-07-05T12:02:19.968Z","body_md":"[[DEF-SET-062|二項関係 \$\\,\\mathcal R=(\\,X,Y,R\\,)\$]] に対して、\n\n\\[\n\\operatorname{src}(\\mathcal R)\\coloneqq X\n\\]\n\nを \$\\mathcal R\$ の **始域** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal R=(X,Y,R),\\quad \\operatorname{src}(\\mathcal R)\\coloneqq X\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-064","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-064","slug":"relation-codomain-definition","title":"終域","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":64,"created_at":"2026-07-05T12:02:19.968Z","updated_at":"2026-07-05T12:02:19.968Z","body_md":"[[DEF-SET-062|二項関係 \$\\,\\mathcal R=(\\,X,Y,R\\,)\$]] に対して、\n\n\\[\n\\operatorname{tgt}(\\mathcal R)\\coloneqq Y\n\\]\n\nを \$\\mathcal R\$ の **終域** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal R=(X,Y,R),\\quad \\operatorname{tgt}(\\mathcal R)\\coloneqq Y\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-065","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-065","slug":"relation-graph-definition","title":"グラフ","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":65,"created_at":"2026-07-05T12:02:19.968Z","updated_at":"2026-07-05T12:02:19.968Z","body_md":"[[DEF-SET-062|二項関係 \$\\,\\mathcal R=(\\,X,Y,R\\,)\$]] に対して、\n\n\\[\n\\operatorname{grf}(\\mathcal R)\\coloneqq R\n\\]\n\nを \$\\mathcal R\$ の **グラフ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mathcal R=(X,Y,R),\\quad \\operatorname{grf}(\\mathcal R)\\coloneqq R\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-066","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-066","slug":"relation-domain-definition","title":"定義域","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":66,"created_at":"2026-07-05T12:02:19.968Z","updated_at":"2026-07-05T12:02:19.968Z","body_md":"[[DEF-SET-062|二項関係 \$\\,\\mathcal R=(\\,X,Y,R\\,)\$]] に対して、\n\n\\[\n\\operatorname{dom}(\\mathcal R)\\coloneqq\\{\\,x\\in X\\mid \\exists y\\in Y\\quad (\\,(x,y)\\in R)\\,)\\,\\}\n\\]\n\nを \$\\mathcal R\$ の **定義域** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\operatorname{dom}(\\mathcal R)\\coloneqq\\{\\,x\\in\\operatorname{src}(\\mathcal R)\\mid \\exists y\\in\\operatorname{tgt}(\\mathcal R)\\quad (\\,(x,y)\\in\\operatorname{grf}(\\mathcal R)\\,)\\,\\}\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-067","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-067","slug":"relation-image-definition","title":"値域","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":67,"created_at":"2026-07-05T12:02:19.968Z","updated_at":"2026-07-05T12:02:19.968Z","body_md":"[[DEF-SET-062|二項関係 \$\\,\\mathcal R=(\\,X,Y,R\\,)\$]] に対して、\n\n\\[\n\\operatorname{img}(\\mathcal R)\\coloneqq\\{\\,y\\in Y\\mid \\exists x\\in X\\quad ((x,y)\\in R)\\,\\}\n\\]\n\nを \$\\mathcal R\$ の **値域** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\operatorname{img}(\\mathcal R)\\coloneqq\\{\\,y\\in\\operatorname{tgt}(\\mathcal R)\\mid \\exists x\\in\\operatorname{src}(\\mathcal R)\\quad ((x,y)\\in\\operatorname{grf}(\\mathcal R))\\,\\}\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-068","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-068","slug":"correspondence-definition","title":"対応","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":68,"created_at":"2026-07-01T03:36:03.596Z","updated_at":"2026-07-01T03:36:03.596Z","body_md":"[[DEF-SET-062|二項関係 \$\\,\\mathcal C=(\\,X,Y,C\\,)\$]] について [[DEF-SET-066|\$\\operatorname{dom}(\\mathcal C)\$]] \$=X\$ であるとき、\$\\mathcal C\$ を \$X\$ から \$Y\$ への **対応** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\operatorname{dom}(\\mathcal C)=\\operatorname{src}(\\mathcal C)\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-069","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-069","slug":"corresponds-definition","title":"対応する","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":69,"created_at":"2026-07-01T03:36:03.596Z","updated_at":"2026-07-01T03:36:03.596Z","body_md":"[[DEF-SET-068|対応 \$\\,\\mathcal C\$]] について [[DEF-SET-065|\$(x,y)\\in \\operatorname{grf}(\\mathcal C)\$]] であるとき、\$\\mathcal C\$ によって \$x\$ に \$y\$ が **対応する** という。","detail_md":null,"logical_statement_md":"\\[\n(x,y)\\in \\operatorname{grf}(\\mathcal C)\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-070","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-070","slug":"map-definition","title":"写像","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":70,"created_at":"2026-07-01T03:36:03.596Z","updated_at":"2026-07-01T03:36:03.596Z","body_md":"\$f\$ を \$X\$ から \$Y\$ への [[DEF-SET-068|対応]] とする。\n\n任意の \$x\\in X\$ に対して、\$f\$ によって \$x\$ に[[DEF-SET-069|対応する|link]] \$y\\in Y\$ がただひとつ[[DEF-SYMBOL-302|存在する|link]]とき、\n\n\$f\$ を \$X\$ から \$Y\$ への **写像** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\forall x\\in \\operatorname{src}(f),\\ \\exists!y\\in \\operatorname{tgt}(f),\\ (x,y)\\in \\operatorname{grf}(f)\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-071","topic_id":"topic-set-theory","subtopic":"maps-and-functions","subtopic_title":"写像","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-071","slug":"map-value-definition","title":"写像の値","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":71,"created_at":"2026-07-01T03:36:03.596Z","updated_at":"2026-07-01T03:36:03.596Z","body_md":"[[DEF-SYMBOL-100|\$f\\colon X\\to Y\$]] によって \$x\\in X\$ に対応する \$y\\in Y\$ を \$x\$ における \$f\$ の **値** とよび、\$f(x)\$ と書く。","detail_md":null,"logical_statement_md":"\\[\nf(x)\n\\]","notation_md":null,"listed":true},{"id":"def-def-symbol-100","topic_id":"topic-words-and-symbols","subtopic":"symbols","subtopic_title":"記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-100","slug":"map-symbol","title":"写像記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":100,"created_at":"2026-07-01T22:27:48.350Z","updated_at":"2026-07-01T22:27:48.350Z","body_md":"\$f\$ が \$X\$ から \$Y\$ への [[DEF-SET-070|写像]] であることを \$f\\colon X\\to Y\$ と書く。","detail_md":null,"logical_statement_md":"\\[\nf\\colon X\\to Y\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-130","topic_id":"topic-set-theory","subtopic":"ordered-pairs","subtopic_title":"順序対","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-130","slug":"tuple-definition","title":"組","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":130,"created_at":"2026-07-08T11:47:00.220Z","updated_at":"2026-07-08T11:47:00.220Z","body_md":"集合 \$a_1,\\ldots,a_n\\, (\\, n\\in\\mathbb{N_{\\ge1}}\\,)\$ に対して、\n\n\$(a_1,\\ldots,a_n)\\coloneqq\\,\$[[|\$\\left\\{\\,\\operatorname{K}\\lbrack 1,a_{1}\\rbrack,\\ldots,\\operatorname{K}\\lbrack n,a_{n}\\rbrack\\,\\right\\}\$|text]]\nを \$n\$ **個の組** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n(a_1,\\ldots,a_n)\\coloneqq\n\\left\\{\\,\\operatorname{K}\\lbrack 1,a_{1}\\rbrack,\\ldots,\\operatorname{K}\\lbrack n,a_{n}\\rbrack\\,\\right\\}\n\\]","notation_md":null,"listed":true},{"id":"def-def-set-131","topic_id":"topic-set-theory","subtopic":"ordered-pairs","subtopic_title":"順序対","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SET-131","slug":"tuple-component-definition","title":"組の成分","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":131,"created_at":"2026-07-08T11:47:00.220Z","updated_at":"2026-07-08T11:47:00.220Z","body_md":"\$T\$ を [[DEF-SET-130|\$n\\,\$個の組]] とする。\n\n\$i\\in\\{\\,1,\\ldots,n\\,\\}\$ に対して、\n\n\\[\n\\operatorname{K}\\lbrack i,x\\rbrack \\in T\n\\]\n\nをみたす \$x\$ を **\$T\$ の第 \$i\$ 成分** とよぶ。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":true},{"id":"def-def-symbol-200","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-200","slug":"operation-symbols","title":"演算記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":200,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[DEF-SYMBOL-201|\$+\$|ref]] [[DEF-SYMBOL-202|\$-\$|ref]] [[DEF-SYMBOL-221|\$\\pm\$|ref]] [[DEF-SYMBOL-222|\$\\mp\$|ref]] [[DEF-SYMBOL-203|\$\\times\$|ref]] [[DEF-SYMBOL-210|\$\\cdot\$|ref]] [[DEF-SYMBOL-204|\$\\div\$|ref]] [[DEF-SYMBOL-215|\$\\sqrt{}\$|ref]]\n\n[[DEF-SYMBOL-205|\$\\sum\$|ref]] [[DEF-SYMBOL-206|\$\\prod\$|ref]] [[DEF-SYMBOL-229|\$\\coprod\$|ref]] [[DEF-SYMBOL-228|\$\\amalg\$|ref]]\n[[DEF-SYMBOL-208|\$\\partial\$|ref]] [[DEF-SYMBOL-209|\$\\nabla\$|ref]] [[DEF-SYMBOL-207|\$\\int\$|ref]] [[DEF-SYMBOL-224|\$\\oint\$|ref]]\n\n[[DEF-SYMBOL-216|\$\\cup\$|ref]] [[DEF-SYMBOL-225|\$\\sqcup\$|ref]] [[DEF-SYMBOL-227|\$\\uplus\$|ref]] [[DEF-SYMBOL-217|\$\\bigcup\$|ref]] [[DEF-SYMBOL-226|\$\\bigsqcup\$|ref]] [[DEF-SYMBOL-218|\$\\cap\$|ref]] [[DEF-SYMBOL-230|\$\\sqcap\$|ref]] [[DEF-SYMBOL-219|\$\\bigcap\$|ref]] \n \n\n[[DEF-SYMBOL-220|\$\\setminus\$|ref]]\n[[DEF-SYMBOL-211|\$\\circ\$|ref]] [[DEF-SYMBOL-212|\$\\ast\$|ref]] [[DEF-SYMBOL-213|\$\\star\$|ref]] [[DEF-SYMBOL-223|\$\\oplus\$|ref]] [[DEF-SYMBOL-214|\$\\otimes\$|ref]]","detail_md":null,"logical_statement_md":"\\[\n\\begin{array}{cccccccc}\n+&-&\\pm&\\mp&\\times&\\cdot&\\div&\\sqrt{}\\\\\n\\sum&\\prod&\\coprod&\\amalg&\\partial&\\nabla&\\int&\\oint\\\\\n\\cup&\\sqcup&\\uplus&\\bigcup&\\bigsqcup&\\cap&\\sqcap&\\bigcap\\\\\n\\setminus&\\circ&\\ast&\\star&\\oplus&\\otimes\n\\end{array}\n\\]","notation_md":null,"listed":true},{"id":"def-def-symbol-201","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-201","slug":"plus-symbol","title":"プラス","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":201,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$+\$|text]] を **プラス** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n+\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-202","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-202","slug":"minus-symbol","title":"マイナス","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":202,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$-\$|text]] を **マイナス** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n-\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-203","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-203","slug":"multiplication-symbol","title":"かける","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":203,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\times\$|text]] を **かける** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\times\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-204","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-204","slug":"division-symbol","title":"わる","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":204,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\div\$|text]] を **わる** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\div\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-205","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-205","slug":"summation-symbol","title":"総和記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":205,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\sum\$|text]] を **総和記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\sum\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-206","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-206","slug":"product-symbol","title":"総乗記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":206,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\prod\$|text]] を **総乗記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\prod\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-207","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-207","slug":"integral-symbol","title":"積分記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":207,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\int\$|text]] を **積分記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\int\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-208","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-208","slug":"partial-symbol","title":"偏微分記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":208,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\partial\$|text]] を **偏微分記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\partial\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-209","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-209","slug":"nabla-symbol","title":"ナブラ","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":209,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\nabla\$|text]] を **ナブラ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\nabla\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-210","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-210","slug":"dot-symbol","title":"ドット","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":210,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\cdot\$|text]] を **ドット** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\cdot\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-211","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-211","slug":"small-circle-symbol","title":"小丸","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":211,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\circ\$|text]] を **小丸** 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とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\coprod\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-230","topic_id":"topic-words-and-symbols","subtopic":"operation-symbols","subtopic_title":"演算記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-230","slug":"square-cap-symbol","title":"スクエアキャップ","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":230,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\sqcap\$|text]] を **スクエアキャップ** 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[[DEF-SYMBOL-314|\$\\Longleftrightarrow\$|ref]]","detail_md":null,"logical_statement_md":"\\[\n\\begin{array}{cccccccc}\n\\forall&\\exists&\\neg&\\land&\\lor&\\to&\\leftarrow&\\leftrightarrow\\\\\n\\Rightarrow&\\Leftarrow&\\Leftrightarrow&\\Longrightarrow&\\Longleftarrow&\\Longleftrightarrow\n\\end{array}\n\\]","notation_md":null,"listed":true},{"id":"def-def-symbol-301","topic_id":"topic-words-and-symbols","subtopic":"logical-symbols","subtopic_title":"論理記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-301","slug":"universal-quantifier","title":"全称記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":301,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\forall\$|text]] を **全称記号** 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とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\propto\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-425","topic_id":"topic-words-and-symbols","subtopic":"relation-symbols","subtopic_title":"関係記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-425","slug":"parallel-symbol","title":"平行記号","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":425,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\parallel\$|text]] を **平行記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\parallel\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-426","topic_id":"topic-words-and-symbols","subtopic":"relation-symbols","subtopic_title":"関係記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-426","slug":"perpendicular-symbol","title":"垂直記号","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":426,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\perp\$|text]] を **垂直記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\perp\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-427","topic_id":"topic-words-and-symbols","subtopic":"relation-symbols","subtopic_title":"関係記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-427","slug":"satisfaction-symbol","title":"充足記号","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":427,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\models\$|text]] を **充足記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\models\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-428","topic_id":"topic-words-and-symbols","subtopic":"relation-symbols","subtopic_title":"関係記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-428","slug":"similar-or-equal-symbol","title":"相似イコール","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":428,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\simeq\$|text]] を **相似イコール** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\simeq\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-800","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-800","slug":"other-symbols","title":"その他記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":800,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[DEF-SYMBOL-802|\$\\varnothing\$|ref]] [[DEF-SYMBOL-802|\$\\emptyset\$|ref]] [[DEF-SYMBOL-801|\$\\infty\$|ref]] [[DEF-SYMBOL-805|\$\\angle\$|ref]]\n\n[[DEF-OTL-001|\$\\aleph\$|ref]] [[DEF-OTL-002|\$\\beth\$|ref]] [[DEF-OTL-003|\$\\gimel\$|ref]] [[DEF-OTL-004|\$\\daleth\$|ref]]\n\n[[DEF-OTL-005|\$\\ell\$|ref]] [[DEF-OTL-006|\$\\imath\$|ref]] [[DEF-OTL-007|\$\\jmath\$|ref]] [[DEF-OTL-008|\$\\hbar\$|ref]] [[DEF-OTL-009|\$\\wp\$|ref]]\n\n[[DEF-OTL-010|\$\\Re\$|ref]] [[DEF-OTL-011|\$\\Im\$|ref]]","detail_md":null,"logical_statement_md":"\\[\n\\begin{array}{ccccc}\n\\varnothing&\\emptyset&\\infty&\\angle\\\\\n\\aleph&\\beth&\\gimel&\\daleth\\\\\n\\ell&\\imath&\\jmath&\\hbar&\\wp\\\\\n\\Re&\\Im\n\\end{array}\n\\]","notation_md":null,"listed":true},{"id":"def-def-symbol-801","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-801","slug":"infinity-symbol","title":"無限大記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":801,"created_at":"2026-07-27T03:36:52.845Z","updated_at":"2026-07-27T03:36:52.845Z","body_md":"[[|\$\\infty\$|text]] を **無限大記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\infty\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-802","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-802","slug":"empty-set-symbol","title":"空集合記号","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":802,"created_at":"2026-07-01T22:27:48.350Z","updated_at":"2026-07-01T22:27:48.350Z","body_md":"[[|\$\\varnothing\$|text]] と [[|\$\\emptyset\$|text]] を **空集合記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\varnothing\\quad\\emptyset\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-803","topic_id":"topic-words-and-symbols","subtopic":"relation-symbols","subtopic_title":"関係記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-803","slug":"mapsto-symbol","title":"対応矢印","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":803,"created_at":"2026-07-01T22:27:48.350Z","updated_at":"2026-07-01T22:27:48.350Z","body_md":"[[|\$\\mapsto\$|text]] を **対応矢印** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\mapsto\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-804","topic_id":"topic-words-and-symbols","subtopic":"relation-symbols","subtopic_title":"関係記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-804","slug":"long-mapsto-symbol","title":"長対応矢印","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":804,"created_at":"2026-07-01T22:27:48.350Z","updated_at":"2026-07-01T22:27:48.350Z","body_md":"[[|\$\\longmapsto\$|text]] を **長対応矢印** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\longmapsto\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-805","topic_id":"topic-words-and-symbols","subtopic":"other-symbols","subtopic_title":"その他記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-805","slug":"angle-symbol","title":"角記号","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":805,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\angle\$|text]] を **角記号** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\angle\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-900","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-900","slug":"auxiliary-symbols","title":"補助記号","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":900,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[DEF-SYMBOL-901|\$\\,.\\,\$|ref]] [[DEF-SYMBOL-902|\$\\,,\\,\$|ref]] [[DEF-SYMBOL-903|\$\\,:\\,\$|ref]] [[DEF-SYMBOL-904|\$\\,;\\,\$|ref]] [[DEF-SYMBOL-905|\$\\,!\\,\$|ref]] [[DEF-SYMBOL-906|\$!!\$|ref]] [[DEF-SYMBOL-907|\$\\%\$|ref]] [[DEF-SYMBOL-908|\$\\,\\prime\\,\$|ref]]\n\n[[DEF-SYMBOL-914|\$\\,(\\,\\,\\,)\\,\$|ref]] [[DEF-SYMBOL-915|\$\\,\\lbrack\\,\\,\\,\\rbrack\\,\$|ref]] [[DEF-SYMBOL-916|\$\\,\\{\\,\\,\\,\\}\\,\$|ref]] [[DEF-SYMBOL-917|\$\\,\\langle\\,\\,\\,\\rangle\\,\$|ref]] [[DEF-SYMBOL-918|\$\\,\\lfloor\\,\\,\\,\\rfloor\\,\$|ref]] [[DEF-SYMBOL-919|\$\\,\\lceil\\,\\,\\,\\rceil\\,\$|ref]] [[DEF-SYMBOL-912|\$\\,\\lvert\\,\\,\\,\\rvert\\,\$|ref]] [[DEF-SYMBOL-913|\$\\,\\lVert\\,\\,\\,\\rVert\\,\$|ref]]\n\n[[DEF-SYMBOL-909|\$\\,/\\,\$|ref]] [[DEF-SYMBOL-910|\$\\,\\backslash\\,\$|ref]] [[DEF-SYMBOL-911|\$\\ldots\$|ref]] [[DEF-SYMBOL-920|\$\\cdots\$|ref]] [[DEF-SYMBOL-921|\$\\vdots\$|ref]] [[DEF-SYMBOL-922|\$\\ddots\$|ref]]","detail_md":null,"logical_statement_md":"\\[\n\\begin{array}{cccccccc}\n\\,.\\,&\\,,\\,&\\,:\\,&\\,;\\,&\\,!\\,&!!&\\%&\\,\\prime\\,\\\\\n\\,(\\,\\,\\,)\\,&\\,\\lbrack\\,\\,\\,\\rbrack\\,&\\,\\{\\,\\,\\,\\}\\,&\\,\\langle\\,\\,\\,\\rangle\\,&\\,\\lfloor\\,\\,\\,\\rfloor\\,&\\,\\lceil\\,\\,\\,\\rceil\\,&\\,\\lvert\\,\\,\\,\\rvert\\,&\\,\\lVert\\,\\,\\,\\rVert\\,\\\\\n\\,/\\,&\\,\\backslash\\,&\\ldots&\\cdots&\\vdots&\\ddots\n\\end{array}\n\\]","notation_md":null,"listed":true},{"id":"def-def-symbol-901","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-901","slug":"period-symbol","title":"ピリオド","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":901,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,.\\,\$|text]] を **ピリオド** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n.\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-902","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-902","slug":"comma-symbol","title":"カンマ","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":902,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,,\\,\$|text]] を **カンマ**、または **コンマ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n,\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-903","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-903","slug":"colon-symbol","title":"コロン","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":903,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,:\\,\$|text]] を **コロン** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n:\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-904","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-904","slug":"semicolon-symbol","title":"セミコロン","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":904,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,;\\,\$|text]] を **セミコロン** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n;\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-905","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-905","slug":"exclamation-mark-symbol","title":"感嘆符","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":905,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,!\\,\$|text]] を **感嘆符** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n!\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-906","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-906","slug":"double-exclamation-mark-symbol","title":"二重感嘆符","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":906,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$!!\$|text]] を **二重感嘆符** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n!!\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-907","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-907","slug":"percent-symbol","title":"パーセント","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":907,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\%\$|text]] を **パーセント** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\%\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-908","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-908","slug":"prime-symbol","title":"プライム","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":908,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,\\prime\\,\$|text]] を **プライム** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\prime\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-909","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-909","slug":"slash-symbol","title":"スラッシュ","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":909,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,/\\,\$|text]] を **スラッシュ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n/\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-910","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-910","slug":"backslash-symbol","title":"バックスラッシュ","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":910,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,\\backslash\\,\$|text]] を **バックスラッシュ** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\backslash\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-911","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-911","slug":"ellipsis-symbol","title":"三点リーダー","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":911,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\ldots\$|text]] を **三点リーダー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\ldots\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-912","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-912","slug":"vertical-bar-symbol","title":"縦棒","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":912,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,\\lvert\\,\$|text]] を **左縦棒**、[[|\$\\,\\rvert\\,\$|text]] を **右縦棒** とよぶ。左縦棒と右縦棒をあわせて **縦棒** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\lvert\\ \\rvert\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-913","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-913","slug":"double-vertical-bar-symbol","title":"二重縦棒","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":913,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,\\lVert\\,\$|text]] を **左二重縦棒**、[[|\$\\,\\rVert\\,\$|text]] を **右二重縦棒** とよぶ。左二重縦棒と右二重縦棒をあわせて **二重縦棒** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\lVert\\ \\rVert\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-914","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-914","slug":"parenthesis-symbol","title":"丸括弧","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":914,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,(\\,\$|text]] を **左丸括弧**、[[|\$\\,)\\,\$|text]] を **右丸括弧** とよぶ。左丸括弧と右丸括弧をあわせて **丸括弧** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n(\\ )\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-915","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-915","slug":"square-bracket-symbol","title":"角括弧","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":915,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,\\lbrack\\,\$|text]] を **左角括弧**、[[|\$\\,\\rbrack\\,\$|text]] を **右角括弧** とよぶ。左角括弧と右角括弧をあわせて **角括弧** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\lbrack\\ \\rbrack\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-916","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-916","slug":"curly-bracket-symbol","title":"波括弧","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":916,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,\\{\\,\$|text]] を **左波括弧**、[[|\$\\,\\}\\,\$|text]] を **右波括弧** とよぶ。左波括弧と右波括弧をあわせて **波括弧** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\{\\ \\}\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-917","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-917","slug":"angle-bracket-symbol","title":"山括弧","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":917,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,\\langle\\,\$|text]] を **左山括弧**、[[|\$\\,\\rangle\\,\$|text]] を **右山括弧** とよぶ。左山括弧と右山括弧をあわせて **山括弧** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\langle\\ \\rangle\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-918","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-918","slug":"floor-bracket-symbol","title":"床括弧","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":918,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,\\lfloor\\,\$|text]] を **左床括弧**、[[|\$\\,\\rfloor\\,\$|text]] を **右床括弧** とよぶ。左床括弧と右床括弧をあわせて **床括弧** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\lfloor\\ \\rfloor\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-919","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-919","slug":"ceiling-bracket-symbol","title":"天井括弧","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":919,"created_at":"2026-07-12T05:24:04.633Z","updated_at":"2026-07-12T05:24:04.633Z","body_md":"[[|\$\\,\\lceil\\,\$|text]] を **左天井括弧**、[[|\$\\,\\rceil\\,\$|text]] を **右天井括弧** とよぶ。左天井括弧と右天井括弧をあわせて **天井括弧** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\lceil\\ \\rceil\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-920","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-920","slug":"centered-ellipsis-symbol","title":"中央三点リーダー","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":920,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\cdots\$|text]] を **中央三点リーダー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\cdots\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-921","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-921","slug":"vertical-ellipsis-symbol","title":"縦三点リーダー","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":921,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\vdots\$|text]] を **縦三点リーダー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\vdots\n\\]","notation_md":null,"listed":false},{"id":"def-def-symbol-922","topic_id":"topic-words-and-symbols","subtopic":"auxiliary-symbols","subtopic_title":"補助記号","subsubtopic":null,"subsubtopic_title":null,"code":"DEF-SYMBOL-922","slug":"diagonal-ellipsis-symbol","title":"斜め三点リーダー","release_channels":["main"],"editing":"on","audit_note":null,"card_design":"normal","order_index":922,"created_at":"2026-10-27T17:27:35.142Z","updated_at":"2026-10-27T17:27:35.142Z","body_md":"[[|\$\\ddots\$|text]] を **斜め三点リーダー** とよぶ。","detail_md":null,"logical_statement_md":"\\[\n\\ddots\n\\]","notation_md":null,"listed":false},{"id":"def-def-tana-993","topic_id":"topic-tana-words","subtopic":null,"subtopic_title":null,"subsubtopic":null,"subsubtopic_title":null,"code":"DEF-TANA-993","slug":"editing-term","title":"編集中カード","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":993,"created_at":"2026-06-29T06:42:02.756Z","updated_at":"2026-06-29T06:42:02.756Z","body_md":"**編集中カード** は、編集中のカードである。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false},{"id":"def-def-tana-994","topic_id":"topic-tana-words","subtopic":null,"subtopic_title":null,"subsubtopic":null,"subsubtopic_title":null,"code":"DEF-TANA-994","slug":"application-card-term","title":"応用カード","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":994,"created_at":"2026-06-29T06:42:02.756Z","updated_at":"2026-06-29T06:42:02.756Z","body_md":"**応用カード** は、応用例を確認するためのカードである。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false},{"id":"def-def-tana-995","topic_id":"topic-tana-words","subtopic":null,"subtopic_title":null,"subsubtopic":null,"subsubtopic_title":null,"code":"DEF-TANA-995","slug":"proof-card-term","title":"証明カード","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":995,"created_at":"2026-06-29T06:42:02.756Z","updated_at":"2026-06-29T06:42:02.756Z","body_md":"**証明カード** は、[[|証明|text]]を確認するためのカードである。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false},{"id":"def-def-tana-996","topic_id":"topic-tana-words","subtopic":null,"subtopic_title":null,"subsubtopic":null,"subsubtopic_title":null,"code":"DEF-TANA-996","slug":"proposition-card-term","title":"命題カード","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":996,"created_at":"2026-06-29T06:42:02.756Z","updated_at":"2026-06-29T06:42:02.756Z","body_md":"**命題カード** は、[[|命題|text]]を確認するためのカードである。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false},{"id":"def-def-tana-997","topic_id":"topic-tana-words","subtopic":null,"subtopic_title":null,"subsubtopic":null,"subsubtopic_title":null,"code":"DEF-TANA-997","slug":"axiom-card-term","title":"公理カード","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":997,"created_at":"2026-06-29T06:42:02.756Z","updated_at":"2026-06-29T06:42:02.756Z","body_md":"**公理カード** は、[[|公理|text]]を確認するためのカードである。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false},{"id":"def-def-tana-998","topic_id":"topic-tana-words","subtopic":null,"subtopic_title":null,"subsubtopic":null,"subsubtopic_title":null,"code":"DEF-TANA-998","slug":"definition-card-term","title":"定義カード","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":998,"created_at":"2026-06-29T06:42:02.756Z","updated_at":"2026-06-29T06:42:02.756Z","body_md":"**定義カード** は、[[|定義|text]]を確認するためのカードである。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false},{"id":"def-def-tana-999","topic_id":"topic-tana-words","subtopic":null,"subtopic_title":null,"subsubtopic":null,"subsubtopic_title":null,"code":"DEF-TANA-999","slug":"dictionary-card-term","title":"辞書カード","release_channels":["main"],"editing":"","audit_note":null,"card_design":"normal","order_index":999,"created_at":"2026-06-29T06:42:02.756Z","updated_at":"2026-06-29T06:42:02.756Z","body_md":"**辞書カード** は、この教材での言葉を確認するためのカードである。","detail_md":null,"logical_statement_md":null,"notation_md":null,"listed":false}],"axioms":[]}],null,null]}] 1a:null 21:[["$","title","0",{"children":"関係記号 | 数学のたな"}],["$","meta","1",{"name":"description","content":"= \\ne \\equiv \\propto \\sim \\simeq \\cong \\approx < \\le\\,\\leqq \\ge\\,\\geqq \\in \\notin \\ni \\not\\ni \\subseteq\\,\\subseteqq \\not\\subseteq\\,\\not\\subseteqq 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関係記号かんけいきごう

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