Maths Cheat Sheet with Latex

Maths Cheat Sheet with Latex#

This is my holy grail document I store in Obsidian that I have for quick reference, either for trying to remember a symbol or if I’m needing the latex name for it. I have a lot of these symbols in my notes, so this is a great way to keep them all in one place. Feel free to download the markdown file yourself and add into your own Obsidian or notion vault.

Relation Operators#

Less Than Relations#

Symbol	LaTeX Command	Comment	Description
\(<\)	`<`	is less than	A is smaller than B
\(\nless\)	`\nless`	is not less than	A is not smaller than B
\(\leq\)	`\leq`	is less than or equal to	A is smaller than or equal to B
\(\leqslant\)	`\leqslant`	is less than or equal to	Alternative form of \(\leq\)
\(\nleq\)	`\nleq`	is neither less than nor equal to	A is not \(\leq\) B
\(\nleqslant\)	`\nleqslant`	is neither less than nor equal to	A is not \(\leqslant\) B
\(\prec\)	`\prec`	precedes	A comes before B in an ordering
\(\nprec\)	`\nprec`	doesn’t precede	A does not precede B
\(\preceq\)	`\preceq`	precedes or equals	A is before or equal to B
\(\npreceq\)	`\npreceq`	neither precedes nor equals	A is neither before nor equal to B
\(\ll\)	`\ll`	much less than	A is significantly smaller than B
\(\lll\)	`\lll`	very much less than	Stronger version of \(\ll\)
\(\subset\)	`\subset`	is a proper subset of	A is a subset but not equal to B
\(\not\subset\)	`\not\subset`	is not a proper subset of	A is not a subset of B
\(\subseteqq\)	`\subseteqq`	is a subset of	A is a subset or equal to B
\(\nsubseteqq\)	`\nsubseteqq`	is not a subset of	A is not a subset or equal to B
\(\sqsubset\)	`\sqsubset`	square subset	A is a subset in some structure
\(\sqsubseteq\)	`\sqsubseteq`	square subset or equals	A is a subset or equal in structure

Greater Than Relations#

Symbol	LaTeX Command	Comment	Description
\(>\)	`>`	is greater than	A is larger than B
\(\ngtr\)	`\ngtr`	is not greater than	A is not larger than B
\(\geq\)	`\geq`	is greater than or equal to	A is larger than or equal to B
\(\geqslant\)	`\geqslant`	is greater than or equal to	Alternative form of \(\geq\)
\(\ngeq\)	`\ngeq`	is neither greater than nor equal to	A is not \(\geq\) B
\(\ngeqslant\)	`\ngeqslant`	is neither greater than nor equal to	A is not \(\geqslant\) B
\(\succ\)	`\succ`	succeeds	A comes after B in an ordering
\(\nsucc\)	`\nsucc`	doesn’t succeed	A does not succeed B
\(\succeq\)	`\succeq`	succeeds or equals	A is after or equal to B
\(\nsucceq\)	`\nsucceq`	neither succeeds nor equals	A is neither after nor equal to B
\(\gg\)	`\gg`	much greater than	A is significantly larger than B
\(\ggg\)	`\ggg`	very much greater than	Stronger version of \(\gg\)
\(\supset\)	`\supset`	is a proper superset of	A is a superset but not equal to B
\(\not\supset\)	`\not\supset`	is not a proper superset of	A is not a superset of B
\(\supseteqq\)	`\supseteqq`	is a superset of	A is a superset or equal to B
\(\nsupseteqq\)	`\nsupseteqq`	is not a superset of	A is not a superset or equal to B
\(\sqsupset\)	`\sqsupset`	square superset	A is a superset in some structure
\(\sqsupseteq\)	`\sqsupseteq`	square superset or equals	A is a superset or equal in structure

Equality and Other Relations#

Symbol	LaTeX Command	Comment	Description
\(=\)	`=`	is equal to	A and B are identical
\(\doteq\)	`\doteq`	approximately equal to	A is equal to B in some sense
\(\equiv\)	`\equiv`	is equivalent to	A and B are equivalent in logic
\(\approx\)	`\approx`	is approximately	A is close to B
\(\cong\)	`\cong`	is congruent to	A is congruent to B (geometry)
\(\simeq\)	`\simeq`	is similar or equal to	A is roughly equal or similar to B
\(\sim\)	`\sim`	is similar to	A is related to B
\(\propto\)	`\propto`	is proportional to	A varies proportionally to B
\(\neq\) or \(\ne\)	`\neq` or `\ne`	is not equal to	A and B are not the same

Additional Operators#

Symbol	LaTeX Command	Comment	Description
\(\parallel\)	`\parallel`	is parallel with	A and B are parallel
\(\nparallel\)	`\nparallel`	is not parallel with	A and B are not parallel
\(\asymp\)	`\asymp`	is asymptotic to	A behaves like B at large scales
\(\bowtie\)	`\bowtie`	bowtie relation	Special relation in algebra
\(\vdash\)	`\vdash`	yields or proves	A proves B in logic
\(\dashv\)	`\dashv`	is reverse yields	Dual of \(\vdash\)
\(\in\)	`\in`	is member of	A belongs to set B
\(\ni\)	`\ni`	owns, has member	B contains A
\(\smile\)	`\smile`	smile relation	Used in geometry
\(\frown\)	`\frown`	frown relation	Used in geometry
\(\models\)	`\models`	models	A models B (logic and sets)
\(\notin\)	`\notin`	is not member of	A is not in set B
\(\perp\)	`\perp`	is perpendicular with	A is perpendicular to B
\(\mid\)	`\mid`	divides	A divides B in number theory

Binary Operators#

Symbol	LaTeX Command	Comment	Description
\(\pm\)	`\pm`	plus or minus	Indicates two possible values, ± A
\(\mp\)	`\mp`	minus or plus	Opposite of \(\pm\)
\(\times\)	`\times`	multiplied by	A × B
\(\div\)	`\div`	divided by	A ÷ B
\(\ast\)	`\ast`	asterisk	Multiplication operator
\(\star\)	`\star`	star	Alternative multiplication notation
\(\dagger\)	`\dagger`	dagger	Used in mathematical proofs
\(\ddagger\)	`\ddagger`	double dagger	Used in mathematical contexts
\(\cap\)	`\cap`	set intersection	Common elements of sets A ∩ B
\(\cup\)	`\cup`	set union	All elements in A or B (A ∪ B)
\(\uplus\)	`\uplus`	multiset addition	Union with multiplicity
\(\sqcap\)	`\sqcap`	square cap	Similar to set intersection
\(\sqcup\)	`\sqcup`	square cup	Similar to set union
\(\vee\)	`\vee`	logical OR	A OR B
\(\wedge\)	`\wedge`	logical AND	A AND B
\(\cdot\)	`\cdot`	dot product	A · B (multiplication or dot product)
\(\diamond\)	`\diamond`	diamond	Used in algebra and logic
\(\bigtriangleup\)	`\bigtriangleup`	big triangle up	Large upright triangle symbol
\(\bigtriangledown\)	`\bigtriangledown`	big triangle down	Large inverted triangle symbol
\(\triangleleft\)	`\triangleleft`	left triangle	Triangle pointing left
\(\triangleright\)	`\triangleright`	right triangle	Triangle pointing right
\(\bigcirc\)	`\bigcirc`	big circle	Large circular operator
\(\bullet\)	`\bullet`	bullet	Used in set notation and logic
\(\wr\)	`\wr`	wreath product	Used in group theory
\(\oplus\)	`\oplus`	direct sum	A ⊕ B (sum of two mathematical structures)
\(\ominus\)	`\ominus`	minus with circle	Alternative subtraction notation
\(\otimes\)	`\otimes`	tensor product	Used in linear algebra
\(\oslash\)	`\oslash`	slash in circle	Used in set theory and logic
\(\odot\)	`\odot`	dot in circle	Used in geometry and algebra
\(\circ\)	`\circ`	small circle	Function composition operator
\(\setminus\)	`\setminus`	set difference	Elements in A but not in B (A \ B)
\(\amalg\)	`\amalg`	amalgamation	Used in algebraic topology

Greek Letters#

Symbol	LaTeX Command	Description
A and α	`\Alpha` and `\alpha`	Capital and lowercase alpha
B and β	`\Beta` and `\beta`	Capital and lowercase beta
Γ and γ	`\Gamma` and `\gamma`	Capital and lowercase gamma
Δ and δ	`\Delta` and `\delta`	Capital and lowercase delta
Ε, ε, ϵ	`\Epsilon`, `\epsilon`, and `\varepsilon`	Standard and variant epsilon
Ζ and ζ	`\Zeta` and `\zeta`	Capital and lowercase zeta
Η and η	`\Eta` and `\eta`	Capital and lowercase eta
Θ, θ, ϑ	`\Theta`, `\theta`, and `\vartheta`	Standard and variant theta
Ι and ι	`\Iota` and `\iota`	Capital and lowercase iota
Κ, κ, ϰ	`\Kappa`, `\kappa`, and `\varkappa`	Standard and variant kappa
Λ and λ	`\Lambda` and `\lambda`	Capital and lowercase lambda
Μ and μ	`\Mu` and `\mu`	Capital and lowercase mu
Ν and ν	`\Nu` and `\nu`	Capital and lowercase nu
Ξ and ξ	`\Xi` and `\xi`	Capital and lowercase xi
Ο and ο	`\Omicron` and `\omicron`	Capital and lowercase omicron
Π, π, ϖ	`\Pi`, `\pi`, and `\varpi`	Standard and variant pi
Ρ, ρ, ϱ	`\Rho`, `\rho`, and `\varrho`	Standard and variant rho
Σ, σ, ς	`\Sigma`, `\sigma`, and `\varsigma`	Standard and final sigma
Τ and τ	`\Tau` and `\tau`	Capital and lowercase tau
Υ and υ	`\Upsilon` and `\upsilon`	Capital and lowercase upsilon
Φ, φ, ϕ	`\Phi`, `\phi`, and `\varphi`	Standard and variant phi
Χ and χ	`\Chi` and `\chi`	Capital and lowercase chi
Ψ and ψ	`\Psi` and `\psi`	Capital and lowercase psi
Ω and ω	`\Omega` and `\omega`	Capital and lowercase omega

Archaic Greek Letters#

Symbol	LaTeX Command	Description
𝔉	`\Digamma`	Archaic Greek letter Digamma
𝔉	`\digamma`	Lowercase Digamma

Unary Operators#

Symbol	LaTeX Command	Comment	Description
+	`+`	plus	Positive sign
-	`-`	negation	Negative sign
\(\neg\)	`\neg`	not	Logical NOT
!	`!`	factorial	Computes factorial (n!)
\(\#\)	`\#`	hash	Used in number theory
\(\#\)	`\#`	primorial	Product of prime numbers

Negated Binary Operators#

Not Equal Relations#

Symbol	LaTeX Command	Comment	Description
\(\neq\) or \(\ne\)	`\neq` or `\ne`	is not equal to	A is different from B
\(\ncong\)	`\ncong`	is not congruent to	A is not congruent to B
\(\nsim\)	`\nsim`	is not similar to	A is not related to B
\(\nshortmid\)	`\nshortmid`	negated short division	A does not divide B
\(\nmid\)	`\nmid`	does not divide	A does not divide B
\(\notin\)	`\notin`	is not a member of	A does not belong to set B

Not Less Than Relations#

Symbol	LaTeX Command	Comment	Description
\(\nless\)	`\nless`	is not less than	A is not smaller than B
\(\nleq\)	`\nleq`	is not less than or equal to	A is neither less than nor equal to B
\(\nleqslant\)	`\nleqslant`	negated less than or equal	Alternative version of \(\nleq\)
\(\nleqq\)	`\nleqq`	negated less than or equal	Alternative notation
\(\lneq\)	`\lneq`	less than but not equal	A < B but not A = B
\(\lvertneqq\)	`\lvertneqq`	strict less than not equal	Stronger version of \(\lneq\)
\(\lnsim\)	`\lnsim`	not similar	A is not similar to B
\(\lnapprox\)	`\lnapprox`	not approximately similar	A is not approximately similar to B
\(\nprec\)	`\nprec`	does not precede	A does not come before B in order
\(\npreceq\)	`\npreceq`	neither precedes nor equals	A is neither before nor equal to B
\(\npreceqq\)	`\npreceqq`	not precedes or equals	Alternative notation
\(\nprecsim\)	`\nprecsim`	not precedes similar	A does not precede B in similarity
\(\nprecnapprox\)	`\nprecnapprox`	not precedes approximately	A does not precede B approximately
\(\ntriangleleft\)	`\ntriangleleft`	not left triangle subset	A is not a left-subset of B
\(\ntrianglelefteq\)	`\ntrianglelefteq`	not left subset equal	A is neither left-subset nor equal
\(\nsubseteq\)	`\nsubseteq`	is not a subset of	A is not contained within B
\(\nsubseteqq\)	`\nsubseteqq`	is not a subset of (variant)	Alternative notation
\(\subsetneq\)	`\subsetneq`	is a subset but not equal	A ⊆ B but A ≠ B
\(\varsupsetneq\)	`\varsupsetneq`	is a superset but not equal	A ⊇ B but A ≠ B

Not Greater Than Relations#

Symbol	LaTeX Command	Comment	Description
\(\ngtr\)	`\ngtr`	is not greater than	A is not larger than B
\(\ngeq\)	`\ngeq`	is not greater than or equal to	A is neither greater than nor equal to B
\(\ngeqslant\)	`\ngeqslant`	negated greater than or equal	Alternative notation
\(\ngeqq\)	`\ngeqq`	negated greater than or equal	Alternative notation
\(\gneq\)	`\gneq`	greater than but not equal	A > B but not A = B
\(\gvertneqq\)	`\gvertneqq`	strict greater than not equal	Stronger version of \(\gneq\)
\(\gnsim\)	`\gnsim`	not similar	A is not similar to B
\(\gnapprox\)	`\gnapprox`	not approximately similar	A is not approximately similar to B
\(\nsucc\)	`\nsucc`	does not succeed	A does not come after B in order
\(\nsucceq\)	`\nsucceq`	neither succeeds nor equals	A is neither after nor equal to B
\(\nsucceqq\)	`\nsucceqq`	not succeeds or equals	Alternative notation
\(\nsuccsim\)	`\nsuccsim`	not succeeds similar	A does not succeed B in similarity
\(\nsuccnapprox\)	`\nsuccnapprox`	not succeeds approximately	A does not succeed B approximately
\(\ntriangleright\)	`\ntriangleright`	not right triangle subset	A is not a right-subset of B
\(\ntrianglerighteq\)	`\ntrianglerighteq`	not right subset equal	A is neither right-subset nor equal
\(\nsupseteq\)	`\nsupseteq`	is not a superset of	A is not containing B
\(\nsupseteqq\)	`\nsupseteqq`	is not a superset of (variant)	Alternative notation
\(\supsetneq\)	`\supsetneq`	is a superset but not equal	A ⊇ B but A ≠ B
\(\supsetneqq\)	`\supsetneqq`	strict superset not equal	Stronger version of \(\supsetneq\)
\(\varsupsetneqq\)	`\varsupsetneqq`	strict superset not equal	Strongest version of \(\supsetneq\)

Other Negated Relations#

Symbol	LaTeX Command	Comment	Description
\(\nvdash\)	`\nvdash`	does not yield	A does not entail B in logic
\(\nvDash\)	`\nvDash`	does not satisfy	A does not model B
\(\nVDash\)	`\nVDash`	does not strongly satisfy	Stronger version of \(\nvDash\)
\(\nshortparallel\)	`\nshortparallel`	not short parallel	A is not parallel to B (short version)
\(\nparallel\)	`\nparallel`	is not parallel with	A is not parallel to B

LaTeX Arrows Reference#

Basic Arrows#

Symbol	LaTeX Command	Description
\(\leftarrow\)	`\leftarrow`	Left arrow
\(\rightarrow\)	`\rightarrow`	Right arrow
\(\leftrightarrow\)	`\leftrightarrow`	Left-right arrow
\(\Leftarrow\)	`\Leftarrow`	Double left arrow
\(\Rightarrow\)	`\Rightarrow`	Double right arrow
\(\Leftrightarrow\)	`\Leftrightarrow`	Double left-right arrow

Long Arrows#

Symbol	LaTeX Command	Description
\(\longleftarrow\)	`\longleftarrow`	Long left arrow
\(\longrightarrow\)	`\longrightarrow`	Long right arrow
\(\longleftrightarrow\)	`\longleftrightarrow`	Long left-right arrow
\(\Longleftarrow\)	`\Longleftarrow`	Long double left arrow
\(\Longrightarrow\)	`\Longrightarrow`	Long double right arrow
\(\Longleftrightarrow\)	`\Longleftrightarrow`	Long double left-right arrow

Curved & Hooked Arrows#

Symbol	LaTeX Command	Description
\(\curvearrowleft\)	`\curvearrowleft`	Curved left arrow
\(\curvearrowright\)	`\curvearrowright`	Curved right arrow
\(\hookleftarrow\)	`\hookleftarrow`	Hooked left arrow
\(\hookrightarrow\)	`\hookrightarrow`	Hooked right arrow

Harpoon Arrows#

Symbol	LaTeX Command	Description
\(\leftharpoonup\)	`\leftharpoonup`	Left harpoon up
\(\leftharpoondown\)	`\leftharpoondown`	Left harpoon down
\(\rightharpoonup\)	`\rightharpoonup`	Right harpoon up
\(\rightharpoondown\)	`\rightharpoondown`	Right harpoon down
\(\upharpoonleft\)	`\upharpoonleft`	Up harpoon left
\(\upharpoonright\)	`\upharpoonright`	Up harpoon right
\(\downharpoonleft\)	`\downharpoonleft`	Down harpoon left
\(\downharpoonright\)	`\downharpoonright`	Down harpoon right

Dotted & Dashed Arrows#

Symbol	LaTeX Command	Description
\(\dashleftarrow\)	`\dashleftarrow`	Dashed left arrow
\(\dashrightarrow\)	`\dashrightarrow`	Dashed right arrow
\(\dotsleftarrow\)	`\dotsleftarrow`	Dotted left arrow
\(\dotsrightarrow\)	`\dotsrightarrow`	Dotted right arrow

Arrows with Lines & Additional Elements#

Symbol	LaTeX Command	Description
\(\twoheadleftarrow\)	`\twoheadleftarrow`	Two-headed left arrow
\(\twoheadrightarrow\)	`\twoheadrightarrow`	Two-headed right arrow
\(\rightsquigarrow\)	`\rightsquigarrow`	Right squiggly arrow
\(\leftrightsquigarrow\)	`\leftrightsquigarrow`	Left-right squiggly arrow
\(\multimap\)	`\multimap`	Multi-map arrow
\(\rightleftharpoons\)	`\rightleftharpoons`	Right-left harpoons
\(\rightrightarrows\)	`\rightrightarrows`	Two right arrows
\(\leftleftarrows\)	`\leftleftarrows`	Two left arrows
\(\upuparrows\)	`\upuparrows`	Two up arrows
\(\downdownarrows\)	`\downdownarrows`	Two down arrows
\(\nwarrow\)	`\nwarrow`	North-west diagonal arrow
\(\nearrow\)	`\nearrow`	North-east diagonal arrow
\(\swarrow\)	`\swarrow`	South-west diagonal arrow
\(\searrow\)	`\searrow`	South-east diagonal arrow

Vertical & Horizontal Arrows#

Symbol	LaTeX Command	Description
\(\uparrow\)	`\uparrow`	Up arrow
\(\downarrow\)	`\downarrow`	Down arrow
\(\updownarrow\)	`\updownarrow`	Up-down arrow
\(\Uparrow\)	`\Uparrow`	Double up arrow
\(\Downarrow\)	`\Downarrow`	Double down arrow
\(\Updownarrow\)	`\Updownarrow`	Double up-down arrow

Miscellaneous Arrows#

Symbol	LaTeX Command	Description
\(\leadsto\)	`\leadsto`	Leads to
\(\mapsto\)	`\mapsto`	Maps to
\(\longmapsto\)	`\longmapsto`	Long maps to
\(\rightarrowtail\)	`\rightarrowtail`	Right tail arrow
\(\leftarrowtail\)	`\leftarrowtail`	Left tail arrow

Maths Cheat Sheet with Latex

Contents

Maths Cheat Sheet with Latex#

Relation Operators#

Less Than Relations#

Greater Than Relations#

Equality and Other Relations#

Additional Operators#

Binary Operators#

Binary Operators#

Greek Letters#

Greek Letters#

Archaic Greek Letters#

Unary Operators#

Unary Operators#

Negated Binary Operators#

Not Equal Relations#

Not Less Than Relations#

Not Greater Than Relations#

Other Negated Relations#

LaTeX Arrows Reference#

Basic Arrows#

Long Arrows#

Curved & Hooked Arrows#

Harpoon Arrows#

Dotted & Dashed Arrows#

Arrows with Lines & Additional Elements#

Vertical & Horizontal Arrows#

Miscellaneous Arrows#