Math Symbols used in Chapter 1

CS390, Fall 2022

Last modified: Jul 23, 2019

Contents:

Abstract

Continuing our goal of being able to actual type and present “proper” mathematics, here are the symbols used in Chapter 1 of the text that were not covered in our earlier basic look at TeX-style mathematics.

1 Boolean Logic

LaTeX	Renders As	meaning
`P \vee Q`	$P \vee Q$	or
`P \wedge Q`	$P \wedge Q$	and
`\neg Q`	$\neg Q$	not
`P \rightarrow Q`	$P \rightarrow Q$	conditional
`P \Rightarrow Q`	$P \Rightarrow Q$	implies
`P \leftrightarrow Q`	$P \leftrightarrow Q$	biconditional
`P \Leftrightarrow Q`	$P \Leftrightarrow Q$	is equivalent to
`\forall x`	$\forall x$	for all
`\exists x`	$\exists x$	there exists

2 Sets

LaTeX	Renders As	meaning
`\cal{N}`	$\cal{N}$	Natural numbers (\cal invokes a caligraphy font)
`\cal{Z}`	$\cal{Z}$	Integers
`\cal{R}`	$\cal{R}$	Real numbers
`\\{ x \\}`	$\{ x \}$	sets
`x \in S`	$x \in S$	member of, is in
`x \notin S`	$x \notin S$	not a member of, is not in
`S \subset T`	$S \subset T$	(strict) subset of
`S \subseteq T`	$S \subseteq T$	subset of or equal to
`S \cup T`	$S \cup T$	union
`S \cap T`	$S \cap T$	intersection
`S \times T`	$S \times T$	cross product
`\bigcup_{i=1}^n S_i`	$\bigcup_{i=1}^n S_i$	union of many sets
`\bigcap_{i=1}^n S_i`	$\bigcup_{i=1}^n S_i$	intersection of many sets

The “big” union and intersection operators are similar to the summation and product operators that we have previously seen.

3 Greek Letters

Greek letters are common in mathematics. In TeX they are obtained by spelling out the name of the letter after a backslash. If you begin the spelled-out name with an upper-case letter, you get the upper-case greek letter:

LaTeX	Renders As	LaTeX	Renders As
`\alpha`	$\alpha$	`A`	$A$
`\beta`	$\beta$	`B`	$B$
`\gamma`	$\gamma$	`\Gamma`	$\Gamma$
`\delta`	$\delta$	`\Delta`	$\Delta$
`\epsilon`	$\epsilon$	`E`	$E$
`\zeta`	$\zeta$	`Z`	$Z$
`\eta`	$\eta$	`H`	$H$
`\theta`	$\theta$	`\Theta`	$\Theta$
`\iota`	$\iota$	`I`	$I$
`\kappa`	$\kappa$	`K`	$K$
`\lambda`	$\lambda$	`\Lambda`	$\Lambda$
`\mu`	$\mu$	`M`	$M$
`\nu`	$\nu$	`N`	$N$
`\xi`	$\xi$	`\Xi`	$\Xi$
`\pi`	$\pi$	`\Pi`	$\Pi$
`\rho`	$\rho$	`R`	$R$
`\sigma`	$\sigma$	`\Sigma`	$\Sigma$
`\tau`	$\tau$	`T`	$T$
`\upsilon`	$\upsilon$	`\Upsilon`	$\Upsilon$
`\phi`	$\phi$	`\Phi`	$\Phi$
`\chi`	$\chi$	`X`	$X$
`\psi`	$\psi$	`\Psi`	$\Psi$
`\omega`	$\omega$	`\Omega`	$\Omega$

The Greek omicron is omitted from the above table as it is indistinguishable from our “O” in both lower and upper case. Similarly, several Greek letters have upper-case forms identical to ours and therefore lack a backslash code.