Operatory, relacje, zbiory

Operatory dwuargumentowe - tworzą wyrażenie z dwóch otaczających je wyrażeń, rozdzielając je krótkim odstępem.
Znak	Kod	Zapis	Odczyt	Znak	Kod	Zapis	Odczyt
\(+\)	+	m+n	\(m+n\)	\(-\)	-	m-n	\(m-n\)
\(\pm\)	\pm	\pm m	\(\pm x\)	\(\mp\)	\mp	\mp m	\(\mp m\)
\(\cdot\)	\cdot	m\cdot n	\(m\cdot n\)	\(\div\)	\div	m\div n	\(m\div n\)
\(\times\)	\times	X\times Y	\(X\times Y\)	\(\setminus\)	\setminus	A\setminus B	\(A\setminus B\)
\(\cup\)	\cup	A\cup B	\(A\cup B\)	\(\cap\)	\cap	A\cap B	\(A\cap B\)
\(\sqcup\)	\sqcup	A\sqcup B	\(A\sqcup B\)	\(\sqcap\)	\sqcap	A\sqcap B	\(A\sqcap B\)
\(\oplus\)	\oplus	A\oplus B	\(A\oplus B\)	\(\boxdot\)	\boxdot	A\boxdot B	\(A\boxdot B\)
\(\ominus\)	\ominus	A\ominus B	\(A\ominus B\)	\(\odot\)	\odot	A\odot B	\(A\odot B\)
\(\vee\)	\vee	p\vee q	\(p\vee q\)	\(\lor\)	\lor	p\lor q	\(p\lor q\)
\(\wedge\)	\wedge	p\wedge q	\(p\wedge q\)	\(\land\)	\land	p\land q	\(p\land q\)
\(\ast\)	\ast	f\ast g	\(f\ast g\)	\(\circ\)	\circ	f\circ g	\(f\circ g\)

cd
Znak	Kod	Znak	Kod	Znak	Kod	Znak	Kod
\(\oslash\)	\oslash	\(\otimes\)	\otimes	\(\triangleleft\)	\triangleleft	\(\triangleright\)	\triangleright
\(\star\)	\star	\(\bullet\)	\bullet	\(\diamond\)	\diamond	\(\uplus\)	\uplus
\(\bigcirc\)	\bigcirc	\(\amalg\)	\amalg	\(\bigtriangleup\)	\bigtriangleup	\(\bigtriangledown\)	\bigtriangledown
\(\dagger\)	\dagger	\(\lhd\)	\lhd	\(\rhd\)	\rhd	\(\ddagger\)	\ddagger
\(\unlhd\)	\unlhd	\(\unrhd\)	\unrhd	\(\wr\)	\wr	\(\smallsetminus\)	\smallsetminus

Symbole zmiennej wielkości
Znak	Kod	Znak	Kod	Znak	Kod	Znak	Kod
\(\sum\)	\sum	\(\bigcup\)	\bigcup	\(\bigvee\)	\bigvee	\(\bigoplus\)	\bigoplus
\(\prod\)	\prod	\(\bigcap\)	\bigcap	\(\bigwedge\)	\bigwedge	\(\bigotimes\)	\bigotimes
\(\coprod\)	\coprod	\(\bigsqcup\)	\bigsqcup	\(\bigodot\)	\bigodot	\(\int\)	\int
\(\oint\)	\oint	\(\biguplus\)	\biguplus	\(\)		\(\)

W akapicie wyglądają one tak:\(\bigwedge_{n\in\mathbf{N}} \bigvee_y \sum_{i=0}^\infty i^2\), natomiast wierszu eksponowanym - tak: \[\bigwedge_{n\in\mathbf{N}} \bigvee_y \sum_{i=0}^\infty i^2\]
Symbole relacji - odstępy miedzy wyrażeniami są szerokie.
Znak Kod Zapis Odczyt Znak Kod Zapis Odczyt
\(\lt\) \lt x\lt y \(x\lt y\) \(\gt\) \gt x\gt y \(x\gt y\)
\(\le\) \le x\le y \(x\le y\) \(\ge\) \ge x\ge y \(x\ge y\)
\(\leqslant\) \leqslant x \leqslant y \(x \leqslant y\) \(\geqslant\) \geqslant x \geqslant y \(x \geqslant y\)
\(\leqq\) \leqq x\leqq y \(x\leqq y\) \(\geqq\) \geqq x\geqq y \(x\geqq y\)
\(\eqslantless\) \eqslantless x\eqslantless y \(x\eqslantless y\) \(\eqslantgtr\) \eqslantgtr x\eqslantgtr y \(x\eqslantgtr y\)
\(\ll\) \ll x\ll y \(x\ll y\) \(\gg\) \gg x\gg y \(x\gg y\)
\(\lll\) \lll x\lll y \(x\lll y\) \(\ggg\) \ggg x\ggg y \(x\ggg y\)
\(\lesssim\) \lesssim x\lesssim y \(x\lesssim y\) \(\gtrsim\) \gtrsim x\gtrsim y \(x\gtrsim y\)
\(\lessapprox\) \lessapprox x\lessapprox y \(x\lessapprox y\) \(\gtrapprox\) \gtrapprox x\gtrapprox y \(x\gtrapprox y\)
\(\lessdot\) \lessdot x\lessdot y \(x\lessdot y\) \(\gtrdot\) \gtrdot x\gtrdot y \(x\gtrdot y\)
\(=\) = x=y \(x=y\) \(\sim\) \sim x\sim y \(x\sim y\)
\(\backsim\) \backsim x\backsim y \(x\backsim y\) \(\simeq\) \simeq x\simeq y \(x\simeq y\)
\(\cong\) \cong x\cong y \(x\cong y\) \(\approx\) \approx x\approx y \(x\approx y\)
\(\approxeq\) \approxeq x\approxeq y \(x\approxeq y\) \(\backsimeq\) \backsimeq x\backsimeq y \(x\backsimeq y\)
\(\propto\) \propto x\propto y \(x\propto y\) \(\equiv\) \equiv x\equiv y \(x\equiv y\)
\(\in\) \in a\in A \(a\in A\) \(i\) i Ai a \(Ai a\)
\(\otin\) otin aotin A \(\aotin A\) \(\) \(\)
Symbole relacji - cd
Znak Kod Znak Kod Znak Kod Znak Kod
\(\lessgtr\) \lessgtr \(\gtrless\) \gtrless \(\lesseqgtr \) \lesseqgtr \(\gtreqless\) \gtreqless
\(\lesseqqgtr\) \lesseqqgtr \(\gtreqqless\) \gtreqqless \(\Bumpeq\) \Bumpeq \(\bumpeq\) \bumpeq
\(\doteqdot\) \doteqdot \(\Doteq\) \Doteq \(\risingdotseq\) \risingdotseq \(\fallingdotseq\) \fallingdotseq
\(\eqcirc\) \eqcirc \(\circeq\) \circeq \(\triangleq\) \triangleq \(\between\) \between
\(\prec\) \prec \(\succ\) \succ \(\precsim\) \precsim \(\succsim\) \succsim
\(\preccurlyeq\) \preccurlyeq \(\succcurlyeq\) \succcurlyeq \(\curlyeqprec\) \curlyeqprec \(\curlyeqsucc\) \curlyeqsucc
\(\precapprox\) \precapprox \(\succapprox\) \succapprox \(\vDash\) \vDash \(\Vdash\) \Vdash
\(\Vvdash\) \Vvdash \(\backepsilon\) \backepsilon \(\therefore\) \therefore \(\because\) \because
\(\varpropto\) \varpropto \(\shortmid\) \shortmid \(\shortparallel\) \shortparallel \(\pitchfork\) \pitchfork
\(\smallsmile\) \smallsmile \(\smallfrown\) \smallfrown \(\vartriangleleft\) \vartriangleleft \(\vartriangleright\) \vartriangleright
\(\blacktriangleleft\) \blacktriangleleft \(\blacktriangleright\) \blacktriangleright \(\trianglelefteq\) \trianglelefteq \(\trianglerighteq\) \trianglerighteq
\(\dotplus\) \dotplus \(\centerdot\) \centerdot \(\intercal\) \intercal \(\ltimes\) \ltimes
\(\rtimes\) \rtimes \(\divideontimes\) \divideontimes \(\Cup\) \Cup \(\doublecup\) \doublecup
\(\Cap\) \Cap \(\doublecap\) \doublecap \(\smallsetminus\) \smallsetminus \(\veebar\) \veebar
\(\barwedge\) \barwedge \(\doublebarwedge\) \doublebarwedge \(\boxplus\) \boxplus \(\boxminus\) \boxminus
\(\circleddash\) \circleddash \(\boxtimes\) \boxtimes \(\boxdot\) \boxdot \(\circledcirc\) \circledcirc
\(\leftthreetimes\) \leftthreetimes \(\rightthreetimes \) \rightthreetimes \(\circledast\) \circledast \(\curlyvee\) \curlyvee
\(\curlywedge\) \curlywedge \(\) \(\) \(\)
Podzbiory
Znak Kod Zapis Odczyt Znak Kod Zapis Odczyt
\(\subset\) subset A \subset B \(A \subset B\) \(\supset\) supset A \supset B \(A \supset B\)
\(\subseteq\) subseteq A \subseteq B \(A \subseteq B\) \(\supseteq\) supseteq A \supseteq B \(A \supseteq B\)
\(\subseteqq\) subseteqq A \subseteqq B \(A \subseteqq B\) \(\supseteqq\) supseteqq A \supseteqq B \(A \supseteqq B\)
\(\sqsubset\) sqsubset A \sqsubset B \(A \sqsubset B\) \(\sqsupset\) sqsupset A \sqsupset B \(A \sqsupset B\)
\(\sqsubseteq\) sqsubseteq A \sqsubseteq B \(A \sqsubseteq B\) \(\sqsupseteq\) sqsupseteq A \sqsupseteq B \(A \sqsupseteq B\)
\(\Subset\) Subset A \Subset B \(A \Subset B\) \(\Supset\) Supset A \Supset B \(A \Supset B\)
\(\subseteq\) subseteq A \subseteq B \(A \subseteq B\) \(\supseteq\) supseteq A \supseteq B \(A \supseteq B\)
\(\subsetneq\) subsetneq A \subsetneq B \(A \subsetneq B\) \(\supsetneq\) supsetneq A \supsetneq B \(A \supsetneq B\)
\(\varsubsetneq\) varsubsetneq A \varsubsetneq B \(A \varsubsetneq B\) \(\varsupsetneq\) varsupsetneq A \varsupsetneq B \(A \varsupsetneq B\)
\(\subseteqq\) subseteqq A \subseteqq B \(A \subseteqq B\) \(\supseteqq\) supseteqq A \supseteqq B \(A \supseteqq B\)
\(\subsetneqq\) subsetneqq A \subsetneqq B \(A \subsetneqq B\) \(\supsetneqq\) supsetneqq A \supsetneqq B \(A \supsetneqq B\)
\(\varsubsetneqq\) varsubsetneqq A \varsubsetneqq B \(A \varsubsetneqq B\) \(\varsupsetneqq\) varsupsetneqq A \varsupsetneqq B \(A\varsupsetneqq B\)
Negacje symbolów relacji i strzałek
Znak Kod Znak Kod Znak Kod Znak Kod
\(\less\) less \(\gtr\) gtr \(\lneq\) lneq \(\gneq\) gneq
\(\leq\) leq \(\geq\) geq \(\leqslant\) leqslant \(\geqslant\) geqslant
\(\lneqq\) lneqq \(\gneqq\) gneqq \(\lvertneqq\) lvertneqq \(\gvertneqq\) gvertneqq
\(\leqq\) leqq \(\geqq\) geqq \(\lnsim\) lnsim \(\gnsim\) gnsim
\(\lnapprox\) lnapprox \(\gnapprox\) gnapprox \(\prec\) prec \(\succ\) succ
\(\preceq\) preceq \(\succeq\) succeq \(\precneqq\) precneqq \(\succneqq\) succneqq
\(\precnsim\) precnsim \(\succnsim\) succnsim \(\precnapprox\) precnapprox \(\succnapprox\) succnapprox
\(\subsetneq\) subsetneq \(\supsetneq\) supsetneq \(\varsubsetneq\) varsubsetneq \(\varsupsetneq\) varsupsetneq
\(\varsubsetneqq\) varsubsetneqq \(\varsupsetneqq\) varsupsetneqq \(\subseteqq\) subseteqq \(\supseteqq\) supseteqq
\(\subseteq\) subseteq \(\supseteq\) supseteq \(\subsetneqq\) subsetneqq \(\supsetneqq\) supsetneqq
\(\mid\) mid \(\shortmid\) shortmid \(\parallel\) parallel \(\shortparallel\) shortparallel
\(\sim\) sim \(\cong\) cong \(\vdash\) vdash \(\vDash\) vDash
\(\Vdash\) Vdash \(\VDash\) VDash \(\triangleleft\) triangleleft \(\triangleright\) triangleright
\(\trianglelefteq\) trianglelefteq \(\trianglerighteq\) trianglerighteq \(\leftarrow\) leftarrow \(\rightarrow\) rightarrow
\(\leftrightarrow\) leftrightarrow \(\Leftarrow\) Leftarrow \(\Rightarrow\) Rightarrow \(\Leftrightarrow\) Leftrightarrow

Znak	Kod	Zapis	Odczyt	Znak	Kod	Zapis	Odczyt
\(\lt\)	\lt	x\lt y	\(x\lt y\)	\(\gt\)	\gt	x\gt y	\(x\gt y\)
\(\le\)	\le	x\le y	\(x\le y\)	\(\ge\)	\ge	x\ge y	\(x\ge y\)
\(\leqslant\)	\leqslant	x \leqslant y	\(x \leqslant y\)	\(\geqslant\)	\geqslant	x \geqslant y	\(x \geqslant y\)
\(\leqq\)	\leqq	x\leqq y	\(x\leqq y\)	\(\geqq\)	\geqq	x\geqq y	\(x\geqq y\)
\(\eqslantless\)	\eqslantless	x\eqslantless y	\(x\eqslantless y\)	\(\eqslantgtr\)	\eqslantgtr	x\eqslantgtr y	\(x\eqslantgtr y\)
\(\ll\)	\ll	x\ll y	\(x\ll y\)	\(\gg\)	\gg	x\gg y	\(x\gg y\)
\(\lll\)	\lll	x\lll y	\(x\lll y\)	\(\ggg\)	\ggg	x\ggg y	\(x\ggg y\)
\(\lesssim\)	\lesssim	x\lesssim y	\(x\lesssim y\)	\(\gtrsim\)	\gtrsim	x\gtrsim y	\(x\gtrsim y\)
\(\lessapprox\)	\lessapprox	x\lessapprox y	\(x\lessapprox y\)	\(\gtrapprox\)	\gtrapprox	x\gtrapprox y	\(x\gtrapprox y\)
\(\lessdot\)	\lessdot	x\lessdot y	\(x\lessdot y\)	\(\gtrdot\)	\gtrdot	x\gtrdot y	\(x\gtrdot y\)
\(=\)	=	x=y	\(x=y\)	\(\sim\)	\sim	x\sim y	\(x\sim y\)
\(\backsim\)	\backsim	x\backsim y	\(x\backsim y\)	\(\simeq\)	\simeq	x\simeq y	\(x\simeq y\)
\(\cong\)	\cong	x\cong y	\(x\cong y\)	\(\approx\)	\approx	x\approx y	\(x\approx y\)
\(\approxeq\)	\approxeq	x\approxeq y	\(x\approxeq y\)	\(\backsimeq\)	\backsimeq	x\backsimeq y	\(x\backsimeq y\)
\(\propto\)	\propto	x\propto y	\(x\propto y\)	\(\equiv\)	\equiv	x\equiv y	\(x\equiv y\)
\(\in\)	\in	a\in A	\(a\in A\)	\(i\)	i	Ai a	\(Ai a\)
\(\otin\)	otin	aotin A	\(\aotin A\)	\(\)			\(\)

Znak	Kod	Znak	Kod	Znak	Kod	Znak	Kod
\(\lessgtr\)	\lessgtr	\(\gtrless\)	\gtrless	\(\lesseqgtr \)	\lesseqgtr	\(\gtreqless\)	\gtreqless
\(\lesseqqgtr\)	\lesseqqgtr	\(\gtreqqless\)	\gtreqqless	\(\Bumpeq\)	\Bumpeq	\(\bumpeq\)	\bumpeq
\(\doteqdot\)	\doteqdot	\(\Doteq\)	\Doteq	\(\risingdotseq\)	\risingdotseq	\(\fallingdotseq\)	\fallingdotseq
\(\eqcirc\)	\eqcirc	\(\circeq\)	\circeq	\(\triangleq\)	\triangleq	\(\between\)	\between
\(\prec\)	\prec	\(\succ\)	\succ	\(\precsim\)	\precsim	\(\succsim\)	\succsim
\(\preccurlyeq\)	\preccurlyeq	\(\succcurlyeq\)	\succcurlyeq	\(\curlyeqprec\)	\curlyeqprec	\(\curlyeqsucc\)	\curlyeqsucc
\(\precapprox\)	\precapprox	\(\succapprox\)	\succapprox	\(\vDash\)	\vDash	\(\Vdash\)	\Vdash
\(\Vvdash\)	\Vvdash	\(\backepsilon\)	\backepsilon	\(\therefore\)	\therefore	\(\because\)	\because
\(\varpropto\)	\varpropto	\(\shortmid\)	\shortmid	\(\shortparallel\)	\shortparallel	\(\pitchfork\)	\pitchfork
\(\smallsmile\)	\smallsmile	\(\smallfrown\)	\smallfrown	\(\vartriangleleft\)	\vartriangleleft	\(\vartriangleright\)	\vartriangleright
\(\blacktriangleleft\)	\blacktriangleleft	\(\blacktriangleright\)	\blacktriangleright	\(\trianglelefteq\)	\trianglelefteq	\(\trianglerighteq\)	\trianglerighteq
\(\dotplus\)	\dotplus	\(\centerdot\)	\centerdot	\(\intercal\)	\intercal	\(\ltimes\)	\ltimes
\(\rtimes\)	\rtimes	\(\divideontimes\)	\divideontimes	\(\Cup\)	\Cup	\(\doublecup\)	\doublecup
\(\Cap\)	\Cap	\(\doublecap\)	\doublecap	\(\smallsetminus\)	\smallsetminus	\(\veebar\)	\veebar
\(\barwedge\)	\barwedge	\(\doublebarwedge\)	\doublebarwedge	\(\boxplus\)	\boxplus	\(\boxminus\)	\boxminus
\(\circleddash\)	\circleddash	\(\boxtimes\)	\boxtimes	\(\boxdot\)	\boxdot	\(\circledcirc\)	\circledcirc
\(\leftthreetimes\)	\leftthreetimes	\(\rightthreetimes \)	\rightthreetimes	\(\circledast\)	\circledast	\(\curlyvee\)	\curlyvee
\(\curlywedge\)	\curlywedge	\(\)		\(\)		\(\)

Znak	Kod	Zapis	Odczyt	Znak	Kod	Zapis	Odczyt
\(\subset\)	subset	A \subset B	\(A \subset B\)	\(\supset\)	supset	A \supset B	\(A \supset B\)
\(\subseteq\)	subseteq	A \subseteq B	\(A \subseteq B\)	\(\supseteq\)	supseteq	A \supseteq B	\(A \supseteq B\)
\(\subseteqq\)	subseteqq	A \subseteqq B	\(A \subseteqq B\)	\(\supseteqq\)	supseteqq	A \supseteqq B	\(A \supseteqq B\)
\(\sqsubset\)	sqsubset	A \sqsubset B	\(A \sqsubset B\)	\(\sqsupset\)	sqsupset	A \sqsupset B	\(A \sqsupset B\)
\(\sqsubseteq\)	sqsubseteq	A \sqsubseteq B	\(A \sqsubseteq B\)	\(\sqsupseteq\)	sqsupseteq	A \sqsupseteq B	\(A \sqsupseteq B\)
\(\Subset\)	Subset	A \Subset B	\(A \Subset B\)	\(\Supset\)	Supset	A \Supset B	\(A \Supset B\)
\(\subseteq\)	subseteq	A \subseteq B	\(A \subseteq B\)	\(\supseteq\)	supseteq	A \supseteq B	\(A \supseteq B\)
\(\subsetneq\)	subsetneq	A \subsetneq B	\(A \subsetneq B\)	\(\supsetneq\)	supsetneq	A \supsetneq B	\(A \supsetneq B\)
\(\varsubsetneq\)	varsubsetneq	A \varsubsetneq B	\(A \varsubsetneq B\)	\(\varsupsetneq\)	varsupsetneq	A \varsupsetneq B	\(A \varsupsetneq B\)
\(\subseteqq\)	subseteqq	A \subseteqq B	\(A \subseteqq B\)	\(\supseteqq\)	supseteqq	A \supseteqq B	\(A \supseteqq B\)
\(\subsetneqq\)	subsetneqq	A \subsetneqq B	\(A \subsetneqq B\)	\(\supsetneqq\)	supsetneqq	A \supsetneqq B	\(A \supsetneqq B\)
\(\varsubsetneqq\)	varsubsetneqq	A \varsubsetneqq B	\(A \varsubsetneqq B\)	\(\varsupsetneqq\)	varsupsetneqq	A \varsupsetneqq B	\(A\varsupsetneqq B\)

Znak	Kod	Znak	Kod	Znak	Kod	Znak	Kod
\(\less\)	less	\(\gtr\)	gtr	\(\lneq\)	lneq	\(\gneq\)	gneq
\(\leq\)	leq	\(\geq\)	geq	\(\leqslant\)	leqslant	\(\geqslant\)	geqslant
\(\lneqq\)	lneqq	\(\gneqq\)	gneqq	\(\lvertneqq\)	lvertneqq	\(\gvertneqq\)	gvertneqq
\(\leqq\)	leqq	\(\geqq\)	geqq	\(\lnsim\)	lnsim	\(\gnsim\)	gnsim
\(\lnapprox\)	lnapprox	\(\gnapprox\)	gnapprox	\(\prec\)	prec	\(\succ\)	succ
\(\preceq\)	preceq	\(\succeq\)	succeq	\(\precneqq\)	precneqq	\(\succneqq\)	succneqq
\(\precnsim\)	precnsim	\(\succnsim\)	succnsim	\(\precnapprox\)	precnapprox	\(\succnapprox\)	succnapprox
\(\subsetneq\)	subsetneq	\(\supsetneq\)	supsetneq	\(\varsubsetneq\)	varsubsetneq	\(\varsupsetneq\)	varsupsetneq
\(\varsubsetneqq\)	varsubsetneqq	\(\varsupsetneqq\)	varsupsetneqq	\(\subseteqq\)	subseteqq	\(\supseteqq\)	supseteqq
\(\subseteq\)	subseteq	\(\supseteq\)	supseteq	\(\subsetneqq\)	subsetneqq	\(\supsetneqq\)	supsetneqq
\(\mid\)	mid	\(\shortmid\)	shortmid	\(\parallel\)	parallel	\(\shortparallel\)	shortparallel
\(\sim\)	sim	\(\cong\)	cong	\(\vdash\)	vdash	\(\vDash\)	vDash
\(\Vdash\)	Vdash	\(\VDash\)	VDash	\(\triangleleft\)	triangleleft	\(\triangleright\)	triangleright
\(\trianglelefteq\)	trianglelefteq	\(\trianglerighteq\)	trianglerighteq	\(\leftarrow\)	leftarrow	\(\rightarrow\)	rightarrow
\(\leftrightarrow\)	leftrightarrow	\(\Leftarrow\)	Leftarrow	\(\Rightarrow\)	Rightarrow	\(\Leftrightarrow\)	Leftrightarrow