Math Symbols used in Chapter 1

CS390, Fall 2019

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.