# Math Symbols used in Chapter 1

## CS390, Fall 2019

**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.