Bảng cheat latex pdf

Trọng âm và dấu phụ[sửa]

\dot{a}, \ddot{a}, \acute{a}, \grave{a} a˙,a¨,a´,a`{\displaystyle {\dot {a}},{\ddot {a}},{\acute {a}},{\grave {a} \check{a}, \breve{a}, \tilde{a}, \bar{a} aˇ,a˘,a~,a¯{\displaystyle {\check {a}},{\breve {a}},{\tilde {a}},{\bar {a}} \hat{a}, \widehat{a}, \vec{a} a^,a^,a→{\displaystyle {\hat {a}},{\widehat {a}},{\vec {a}}}

Standard numerical functions[edit]

\exp_a b = a^b, \exp b = e^b, 10^m expa⁡b=ab,exp⁡b=eb,10m{\displaystyle \exp _{a}b=a^{b},\exp b=e^{b},10^{m . s. {\displaystyle \operatorname {sgn} r,\left\vert s\right\vert } \ln c = \log c, \lg d = \log_{10} d ln⁡c=log⁡c,lg⁡d=log10⁡d{\displaystyle \ln c=\log c,\lg d=\log _{10}d} \sin a, \cos b, \tan c, \cot d, \sec f, \csc g sin⁡a,cos⁡b,tan⁡c,cot⁡d,sec⁡f,csc⁡g{\displaystyle \sin a,\cos b,\tan c,\cot d,\sec f,\csc g} \arcsin h, \arccos i, \arctan j arcsin⁡h,arccos⁡i,arctan⁡j{\displaystyle \arcsin h,\arccos i,\arctan j} \sinh k, \cosh l, \tanh m, \coth n sinh⁡k,cosh⁡l,tanh⁡m,coth⁡n{\displaystyle \sinh k,\cosh l,\tanh m,\coth n} \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n sh⁡k,ch⁡l,th⁡m,coth⁡n{\displaystyle \operatorname {sh} k,\operatorname {ch} l,\operatorname {th} m,\operatorname {coth} n} \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q argsh⁡o,argch⁡p,argth⁡q{\displaystyle \operatorname {argsh} o,\operatorname {argch} p,\operatorname {argth} q} \check{a}, \breve{a}, \tilde{a}, \bar{a}0 sgn⁡r,|s|{\displaystyle \operatorname {sgn} r,\left\vert s\right\vert } \check{a}, \breve{a}, \tilde{a}, \bar{a}1 phút(x,y),max(x,y){\displaystyle \min(x

Bounds[edit]

\check{a}, \breve{a}, \tilde{a}, \bar{a}2 minx,maxy,infs,supt{\displaystyle \min x,\max y,\inf s,\sup t} \check{a}, \breve{a}, \tilde{a}, \bar{a}3 limu,lim infv,lim supw{ \check{a}, \breve{a}, \tilde{a}, \bar{a}4 dim⁡p,deg⁡q,detm,ker⁡ϕ{\displaystyle \dim p,\deg q,\det m,\ker \phi }

Projections[edit]

\check{a}, \breve{a}, \tilde{a}, \bar{a}5 Prj,hom⁡l,‖z‖,arg⁡z{\displaystyle \Pr j,\hom l,\lVert z\rVert ,\arg z}

Vi sai

\check{a}, \breve{a}, \tilde{a}, \bar{a}6 dt,dt,∂t,∇ψ{\displaystyle dt,\mathrm {d} t,\partial t,\nabla \psi } \check{a}, \breve{a}, \tilde{a}, \bar{a}7 dy/dx, . ,{\dot {y}},{\ddot {y}}} \check{a}, \breve{a}, \tilde{a}, \bar{a}8 ′,‵,f′,f′,f″,f(3),y˙,y¨{\displaystyle \prime ,\backprime ,f^{\prime },f',f'',f^{(3)}\!,{\dot {y}},{\ddot {y}}}

Các ký hiệu hoặc hằng số dạng chữ cái[sửa]

\check{a}, \breve{a}, \tilde{a}, \bar{a}9 ∞,ℵ,∁,∍,ð,Ⅎ,ℏ{\displaystyle \infty ,\aleph ,\complement ,\backepsilon ,\eth ,\Finv ,\hbar }\hat{a}, \widehat{a}, \vec{a}0 ℑ,ı,ȷ,k,ℓ,℧,℘,ℜ,Ⓢ,§,¶,Å{\displaystyle \Im ,\imath ,\jmath ,\Bbbk ,\ell ,\mho ,\wp ,\Re ,\circledS ,\S ,\P ,\mathrm {\AA} }

Modular arithmetic[edit]

\hat{a}, \widehat{a}, \vec{a}1 sk≡0(modm){\displaystyle s_{k}\equiv 0{\pmod {m}}} \hat{a}, \widehat{a}, \vec{a}2 amodb{\displaystyle a{\bmod {b \hat{a}, \widehat{a}, \vec{a}3 gcd(m,n),lcm⁡(m,n){\displaystyle \gcd(m,n),\operatorname {lcm} (m,n)} \hat{a}, \widehat{a}, \vec{a}4 ∣,∤,∣,∤{\displaystyle \mid ,\nmid ,\shortmid ,\nshortmid }

Radicals[edit]

\hat{a}, \widehat{a}, \vec{a}5 √,2,2n,x3+y323{\displaystyle \surd ,{\sqrt {2}},{\sqrt[{n}]{2}},{\sqrt[{3}]

Operators[edit]

\hat{a}, \widehat{a}, \vec{a}6 +,−,±,∓,∔{\displaystyle +,-,\pm ,\mp ,\dotplus } \hat{a}, \widehat{a}, \vec{a}7 ×,÷,⋇,/,∖ \hat{a}, \widehat{a}, \vec{a}8 ⋅,∗∗,⋆,∘,∙{\displaystyle \cdot ,*\ast ,\star ,\circ ,\bullet } \hat{a}, \widehat{a}, \vec{a}9 ⊞,⊟,⊠,⊡{\displaystyle \boxplus ,\boxminus ,\boxtimes ,\boxdot } \exp_a b = a^b, \exp b = e^b, 10^m0 ⊕,⊖,⊗,⊘,⊙{\displaystyle \oplus ,\ominus ,\otimes ,\oslash ,\odot } \exp_a b = a^b, \exp b = e^b, 10^m1 ⊝,⊚,⊛{\displaystyle \circleddash ,\circledcirc ,\circledast } \exp_a b = a^b, \exp b = e^b, 10^m2 ⨁,⨂,⨀{\displaystyle \bigoplus ,\bigotimes ,\bigodot }

Sets[edit]

\exp_a b = a^b, \exp b = e^b, 10^m3 {},∅∅∅,∅{\displaystyle \{\},\emptyset \emptyset \emptyset ,\varnothing } \exp_a b = a^b, \exp b = e^b, 10^m4 ∈,∉∉,∋,∌ \exp_a b = a^b, \exp b = e^b, 10^m5 ∩,⋒,⊓,⋂{\displaystyle \cap ,\Cap ,\sqcap ,\bigcap } \exp_a b = a^b, \exp b = e^b, 10^m6 ∪,⋓,⊔,⋃,⨆,⊎,⨄{\displaystyle \cup ,\Cup ,\sqcup ,\bigcup ,\bigsqcup ,\uplus ,\biguplus } \exp_a b = a^b, \exp b = e^b, 10^m7 ∖,∖,×{\displaystyle \setminus ,\smallsetminus ,\times } \exp_a b = a^b, \exp b = e^b, 10^m8 ⊂,⋐,⊏{\displaystyle \subset ,\Subset ,\sqsubset } \exp_a b = a^b, \exp b = e^b, 10^m9 ⊃,⋑,⊐{\displaystyle \supset ,\Supset ,\sqsupset } \ln c = \log c, \lg d = \log_{10} d0 ⊆,⊈,⊊,⊊,⊑{\displaystyle \subseteq ,\nsubseteq ,\subsetneq ,\varsubsetneq ,\sqsubseteq } \ln c = \log c, \lg d = \log_{10} d1 ⊇,⊉,⊋,⊋,⊒{\displaystyle \supseteq ,\nsupseteq ,\supsetneq ,\varsupsetneq ,\sqsupseteq } \ln c = \log c, \lg d = \log_{10} d2 ⫅,⊈,⫋,⫋{\displaystyle \subseteqq ,\nsubseteqq ,\subsetneqq ,\varsubsetneqq } \ln c = \log c, \lg d = \log_{10} d3 ⫆,⊉,⫌,⫌{\displaystyle \supseteqq ,\nsupseteqq ,\supsetneqq ,\varsupsetneqq }

Relations[edit]

\ln c = \log c, \lg d = \log_{10} d4 =,≠,≠,≡,≢{\displaystyle =,\neq ,\neq ,\equiv ,\not \equiv } \ln c = \log c, \lg d = \log_{10} d5 \ln c = \log c, \lg d = \log_{10} d6 \ln c = \log c, \lg d = \log_{10} d7 ≐,≑, . ={\displaystyle \doteq ,\doteqdot ,{\overset {\underset {\mathrm {def} }{}}{=}},. =} \ln c = \log c, \lg d = \log_{10} d8 ∼,≁,∽,∼,≃,⋍,≂,≅,≆{\displaystyle \sim ,\nsim ,\backsim ,\thicksim ,\simeq ,\backsimeq , \ln c = \log c, \lg d = \log_{10} d9 ≈,≈,≊,≍,∝,∝{\displaystyle \approx ,\thickapprox ,\approxeq ,\asymp ,\propto ,\varpropto } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g0 <,≮,≪,≪̸,⋘,⋘̸,⋖{\displaystyle <,\nless ,\ll ,\not \ll ,\lll ,\not \lll ,\lessdot } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g1 >,≯,≫,≫̸,⋙,⋙̸,⋗{\displaystyle >,\ngtr ,\gg ,\not \gg ,\ggg ,\not \ggg ,\gtrdot } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g2 ≤,≤,⪇,≦,≰,≰,≨,≨{\displaystyle \leq ,\leq ,\lneq ,\leqq ,\nleq ,\nleqq ,\lneqq ,\lvertneqq } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g3 ≥,≥,⪈,≧,≱,≱,≩,≩{\displaystyle \geq ,\geq ,\gneq ,\geqq ,\ngeq ,\ngeqq ,\gneqq ,\gvertneqq } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g4 ≶,⋚,⪋,≷,⋛,⪌{\displaystyle \lessgtr ,\lesseqgtr ,\lesseqqgtr ,\gtrless ,\gtreqless ,\gtreqqless } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g5 ⩽,⪇,⪕{\displaystyle \leqslant ,\nleqslant ,\eqslantless } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g6 ⩾,⪈,⪖{\displaystyle \geqslant ,\ngeqslant ,\eqslantgtr } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g7 ≲,⋦,⪅,⪉{\displaystyle \lesssim ,\lnsim ,\lessapprox ,\lnapprox } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g8 ≳,⋧,⪆,⪊{\displaystyle \gtrsim ,\gnsim ,\gtrapprox ,\gnapprox } \sin a, \cos b, \tan c, \cot d, \sec f, \csc g9 ≺,⊀,⪯,⋠,⪵{\displaystyle \prec ,\nprec ,\preceq ,\npreceq ,\precneqq } \arcsin h, \arccos i, \arctan j0 ≻,⊁,⪰,⋡,⪶{\displaystyle \succ ,\nsucc ,\succeq ,\nsucceq ,\succneqq } \arcsin h, \arccos i, \arctan j1 ≼,⋞{\displaystyle \preccurlyeq ,\curlyeqprec } \arcsin h, \arccos i, \arctan j2 ≽,⋟{\displaystyle \succcurlyeq ,\curlyeqsucc } \arcsin h, \arccos i, \arctan j3 ≾,⋨,⪷,⪹{\displaystyle \precsim ,\precnsim ,\precapprox ,\precnapprox } \arcsin h, \arccos i, \arctan j4 ≿,⋩,⪸,⪺{\displaystyle \succsim ,\succnsim ,\succapprox ,\succnapprox }

Geometric[edit]

\arcsin h, \arccos i, \arctan j5 ∥,∦,∥,∦{\displaystyle \parallel ,\nparallel ,\shortparallel ,\nshortparallel } \arcsin h, \arccos i, \arctan j6 ⊥,∠,∢,∡,45∘{\ \arcsin h, \arccos i, \arctan j7 ◻,◻,◼,⋄,◊,◊,⧫,★{\displaystyle \Box ,\square ,\blacksquare ,\diamond ,\Diamond ,\lozenge ,\blacklozenge ,\bigstar } \arcsin h, \arccos i, \arctan j8 ◯,△,△,▽{\displaystyle \bigcirc ,\triangle ,\bigtriangleup ,\bigtriangledown } \arcsin h, \arccos i, \arctan j9 △,▽{\displaystyle \vartriangle ,\triangledown } \sinh k, \cosh l, \tanh m, \coth n0 ▴,▾,◂,▸{\displaystyle \blacktriangle ,\blacktriangledown ,\blacktriangleleft ,\blacktriangleright }

Logic[edit]

\sinh k, \cosh l, \tanh m, \coth n1 ∀,∃,∄{\displaystyle \forall ,\exists ,\nexists } \sinh k, \cosh l, \tanh m, \coth n2 ∴,∵,&{\displaystyle \do đó ,\bởi vì ,\And } \sinh k, \cosh l, \tanh m, \coth n3

không sử dụng \sinh k, \cosh l, \tanh m, \coth n4 hiện không được dùng nữa

∨,∨,⋎,⋁{\displaystyle \lor ,\vee ,\curlyvee ,\bigvee } \sinh k, \cosh l, \tanh m, \coth n5

không sử dụng \sinh k, \cosh l, \tanh m, \coth n6 hiện không được dùng nữa

∧,∧,⋏,⋀{\displaystyle \land ,\wedge ,\curlywedge ,\bigwedge } \sinh k, \cosh l, \tanh m, \coth n7

\sinh k, \cosh l, \tanh m, \coth n8

q¯,abc¯,q¯,abc¯,{\displaystyle {\bar {q}},{\bar {abc}},{\overline {q}},{\overline {abc}

¬¬,⧸R,⊥,⊤{\displaystyle \lnot \neg ,\not \operatorname {R} ,\bot ,\top }

Bảng cheat latex pdf

\sinh k, \cosh l, \tanh m, \coth n9 ⊢,⊣,⊨,⊩,⊨{\displaystyle \vdash ,\dashv ,\vDash ,\Vdash ,\models } \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n0 ⊪,⊬,⊮,⊭ \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n1 ⌜⌝⌞⌟{\displaystyle \ulcorner \urcorner \llcorner \lrcorner }

Arrows[edit]

\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n2 ⇛,⇚{\displaystyle \Rrightarrow ,\Lleftarrow } \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n3 ⇒,⇏,⟹,⟹{\displaystyle \Rightarrow ,\nRightarrow ,\Longrightarrow ,\implies } \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n4 ⇐,⇍,⟸{\displaystyle \Leftarrow ,\nLeftarrow ,\Longleftarrow } \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n5 ⇔,⇎,⟺,⟺{\displaystyle \Leftrightarrow ,\nLeftrightarrow ,\Longleftrightarrow ,\iff } \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n6 ⇑,⇓,⇕{\displaystyle \Uparrow ,\Downarrow ,\Updownarrow } \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n7 →→,↛,⟶{\displaystyle \rightarrow \to ,\nrightarrow ,\longrightarrow } \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n8 ←←,↚,⟵{\displaystyle \leftarrow \gets ,\nleftarrow ,\longleftarrow } \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n9 ↔,↮,⟷{\displaystyle \leftrightarrow ,\nleftrightarrow ,\longleftrightarrow } \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q0 ↑,↓,↕{\displaystyle \uparrow ,\downarrow ,\updownarrow } \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q1 ↗,↙,↖,↘{\displaystyle \nearrow ,\swarrow ,\nwarrow ,\searrow } \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q2 ↦,⟼{\displaystyle \mapsto ,\longmapsto } \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q3 ⇀,⇁,↼,↽,↿,↾,⇃,⇂,⇌,⇋{\displaystyle \rightharpoonup ,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft ,\upharpoonright ,\downharpoonleft ,\downharpoonright ,\rightleftharpoons ,\leftrightharpoons } \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q4 ↶,↺,↰,⇈,⇉,⇄,↣,↬{\displaystyle \curvearrowleft ,\circlearrowleft ,\Lsh ,\upuparrows ,\rightrightarrows ,\rightleftarrows ,\rightarrowtail ,\looparrowright } \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q5 ↷,↻,↱,⇊,⇇,⇆,↢,↫{\displaystyle \curvearrowright ,\circlearrowright ,\Rsh ,\downdownarrows ,\leftleftarrows ,\leftrightarrows ,\leftarrowtail ,\looparrowleft } \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q6 ↪,↩,⊸,↭,⇝,↠,↞{\displaystyle \hookrightarrow ,\hookleftarrow ,\multimap ,\leftrightsquigarrow ,\rightsquigarrow ,\twoheadrightarrow ,\twoheadleftarrow }

Special[edit]

\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q7 ⨿¶§%†‡…⋯⋮⋱{\displaystyle \amalg \P \S \%\dagger \ddagger \ldots \cdots \vdots \ddots } \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q8 \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q9 ♢,♡,♣,♠,⅁,♭,♮,♯{\displaystyle \diamondsuit ,\heartsuit ,\clubsuit ,\spadesuit ,\Game ,\flat ,\natural ,\sharp }

Unsorted (new stuff)[edit]

\check{a}, \breve{a}, \tilde{a}, \bar{a}00 ╱,╲,⋅,⋉,⋊,⋋,⋌{\displaystyle \diagup ,\diagdown ,\centerdot ,\ltimes ,\rtimes ,\leftthreetimes ,\rightthreetimes }\check{a}, \breve{a}, \tilde{a}, \bar{a}01 ≖,≗,≜,≏,≎,≑,≓,≒{\displaystyle \eqcirc ,\circeq ,\triangleq ,\bumpeq ,\Bumpeq ,\doteqdot ,\risingdotseq ,\fallingdotseq } \check{a}, \breve{a}, \tilde{a}, \bar{a}02 ⊺,⊼,⊻,⩞,≬,⋔{\displaystyle \intercal ,\barwedge ,\veebar ,\doublebarwedge ,\between ,\pitchfork } \check{a}, \breve{a}, \tilde{a}, \bar{a}03 ⊲,⋪,⊳,⋫{\displaystyle \vartriangleleft ,\ntriangleleft ,\vartriangleright ,\ntriangleright } \check{a}, \breve{a}, \tilde{a}, \bar{a}04 ⊴,⋬,⊵,⋭{\displaystyle \trianglelefteq ,\ntrianglelefteq ,\trianglerighteq ,\ntrianglerighteq }