latex_summary

typesetting

equal align

$$\begin{align*} A &= B + C \\ &= C + D + C \\ &= 2C + D \end{align*}$$

braces

$$f(x)=\left\{ \begin{align} x & = & \cos(t) \\ y & = & \sin(t) \\ z & = & \frac xy \end{align} \right.$$

spaces

-	-	-
a \qquad b	$a \quad b$	two m's width
a \quad b	$a\quad b$	one m's width
a \ b	$a \ b$
a ; b	$a ; b$
a , b	$a , b$
ab	$ab$
a\!b	$a ! b$

Caculus Symbols

• sum $\sum_{i=0}^{n}$

• sum with limits $\sum_\limits{i=0}^{n}$

• product $\prod_{i=1}^{n}$

Others

• vector with arrow $\vec{v}$

• vevtor with bold $\boldsymbol{v}$

• doteq $\doteq$

• prime $w^\prime$

• floor $\lfloor x \rfloor$

• ceil $\lceil x \rceil$

• too less $\ll$

• too geate $\gg$

Operations

• a/b $\frac{a}{b}$

• sqrt $\sqrt{a}$

Logic Symbols

material implcation

• Rightarrow $\Rightarrow$

• to, rightarrow $\rightarrow or \to$

• supset $\supset$

• implies $\implies$

material equivalence

• Leftrightarrow $\Leftrightarrow$

• equiv $\equiv$

• leftrightarrow $\leftrightarrow$

• iff $\iff$

negation

• lnot, neg $\lnot \neg$

• sim $\sim$

domain of discourse

• mathbb $\mathbb{D}$

logical conjunction

• wedge, land $\wedge \land$

• cdot $\cdot$

• & $&$

logical disjunction

• lor, vee $\lor \vee$

• parallel $\parallel$

exclusive disjunction

• oplus $\oplus$

• veebar $\veebar$

tautology and contradition

• top $\top$

• bot $\bot$

quantifications

• forall $\forall$

• exists $\exists$

proves and models

• vdash $\vdash$

• vDash, models $\vDash \models$