Vectors, sets and fonts

Letters in maths come in different styles that mean different things: bold for vectors, blackboard bold for number sets, curly script for special sets and transforms. Each style is a command that wraps the letter.

Vectors

\mathbf{v} makes an upright bold letter, the usual print style for a vector. \vec{v} puts an arrow over the letter, the usual handwritten style.

\mathbf makes Latin letters and digits bold, but not Greek letters. For a bold Greek letter use \boldsymbol: \boldsymbol{\mu} gives $\boldsymbol{\mu}$.

Hats, bars and other accents

• \hat{x} gives $\hat{x}$, as in a unit vector $\hat{\mathbf{n}}$.
• \bar{x} gives $\bar{x}$, as in a mean.
• \tilde{x} gives $\tilde{x}$.
• \overline{AB} draws a line over everything in its braces: $\overline{AB}$.

Number sets

\mathbb gives the blackboard-bold capitals for the number sets: $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$ and $\mathbb{C}$.

Set symbols

• \in gives $\in$, and \notin gives $\notin$.
• \subset gives $\subset$, and \subseteq gives $\subseteq$.
• \cup gives $\cup$, \cap gives $\cap$, and \setminus gives $\setminus$.
• \emptyset gives $\emptyset$.

Set-builder notation puts it together, with the braces from lesson 5:

Logic

\forall gives $\forall$ ("for all"), \exists gives $\exists$ ("there exists"), and \neg gives $\neg$ ("not").

Other maths fonts

• \mathcal{L} gives a script letter, $\mathcal{L}$, used for transforms and some sets.
• \mathrm{...} gives upright letters, $\mathrm{d}$, for units or a d in a derivative.
• \mathsf{...} gives sans serif, $\mathsf{T}$, which some books use for a transpose.

Practise

In short

• \mathbf for bold vectors, \vec for arrows, \boldsymbol for bold Greek letters.
• \hat, \bar, \tilde and \overline for accents.
• \mathbb for number sets, \mathcal for script letters, and \in, \subset, \cup, \cap, \emptyset, \forall, \exists for sets and logic.

Next, in lesson 9: matrices, and functions defined in several parts.