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