useful latex.md

Useful LaTeX Equation Stuff

General

Name	Code	Result
therefore	\therefore	$\therefore$
equivalent to	\equiv	$\equiv$
square root	\sqrt{x}	$\sqrt{x}$
n-th root	\sqrt[n]{x}	$\sqrt[n]{x}$
times	\times or \cdot	" $\times$ " or " $\cdot$ "
not equals	\neq	$\neq$
exponent	x^{something}	$x^{something}$
subscript	x_{something}	$x_{something}$
sumation	\sum_{i=0}^{100}f(i)	$$\sum_{i=0}^{100}f(i)$$
limit	\lim_{x\rightarrow\infty}x	$$\lim_{x\rightarrow\infty}x$$
fraction	\frac{x}{y}	$$\frac{x}{y}$$

Domains

Name	Code	Result	Values
Natural Numbers	\mathbb{N}	$\mathbb{N}$	$0,1,2,3,\ldots$
Whole Numbers	\mathbb{W}	$\mathbb{W}$	Same as Natural for CS2050 purposes
Positive Integers	\mathbb{Z}^+	$\mathbb{Z}^+$	$1,2,3,\ldots$
Integers	\mathbb{Z}	$\mathbb{Z}$	$\ldots,-2,-1,0,1,2,\ldots$
Rational Numbers	\mathbb{Q}	$\mathbb{Q}$	Anyting expressible as a fraction
Irrational Numbers	\mathbb{I}	$\mathbb{I}$	Anything real that isn't rational i.e. $\mathbb{R}-\mathbb{Q}$
Complex Numbers	\mathbb{C}	$\mathbb{C}$	Imaginaryyyyy
Real Numbers	\mathbb{R}	$\mathbb{R}$	Everything not complex

The definition of Natural Numbers varies a lot. For CS 2050, we consider 0 to be a natural number. Some consider 0 not to be, and have $\mathbb{W}$ represent $0,1,2,\ldots$ instead.

Logical Equivalences

Name	Code	Alt Code	Result
Negation	\neg	\lnot	$\neg$
AND	\wedge	\land	$\wedge$
OR	\vee	\lor	$\vee$
XOR	\oplus	\veebar	$\oplus$, $\veebar$
Implies	\rightarrow	\Rightarrow	$\rightarrow, \Rightarrow$
Biconditional / IFF	\leftrightarrow	\Leftrightarrow	$\leftrightarrow$, $\Leftrightarrow$

Note that \veebar requres \usepackage{amssymb} . This should already be imported in our template.

Quantifiers

Name	Code	Result
Forall	\forall	$\forall$
Exists	\exists	$\exists$

Make sure to have a space after each command since \forallx for instance will cause errors.

Sets

Name	Code	Result
Union	\cup	$\cup$
Intersection	\cap	$\cap$
Complement (c)	S^c	$S^c$
Complement (bar)	\bar{S}	$\bar{S}$
Difference	\setminus \\	$\setminus$ (backslash is a special operator) or - just use a minus sign
Empty set	\empty \emptyset \{\}	$\emptyset$ or { }
Power set	\mathbb{P}(S)	$\mathbb{P}(S)$
Element of / in	\in	$\in$
Not element of / not in	\notin	$\notin$

Counting

Name	Code	Alt Code	Result
Binomial Coefficient	{n \atop c}	\binom{n}{c}	$$\binom{n}{c}$$
Multinomial Coefficient	{n \atop a,b,c,d}	\binom{n}{a,b,c,d}	$$\binom{n}{a,b,c,d}$$

Note that \binom{n}{c} requires the import \usepackage{amsmath} . It is already included in our provided templates.