Math Symbols used in Chapter 1
CS390, Spring 2024
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 |
$\bigcap_{i=1}^n S_i$ | 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.