# A Very Brief Introduction to MathJax

To write mathematical expressions in posts or comments on this blog, you can use a piece of software called MathJax.  To write a MathJax formula in your post, you enclose it within special parentheses: for inline formulas (those that appear in the same line as your text), enclose the formula in  $$…$$ and for displayed formulas (those that appear on a line of their own), use $…$ .  These parentheses signal to your browser to run a code snippet that renders your formula in elegant mathematical notation.  (You must have JavaScript enabled in your browser for MathJax to work properly.)

To see how any of the formulas was made, right-click on it and choose “Show Math As > TeX Commands”.  This will show you the MathJax code that was put between the parentheses to generate that expression.

(Note that in some browsers, such as Firefox, the MathJaX right-click menu that contains this command may be obscured by the browser’s own right-click menu. Click somewhere outside the main browser canvas — such as in the address bar — to dismiss the browser menu and reveal the MathJaX one behind it).

1. For inline formulas, enclose the formula in $$…$$. For displayed formulas, use $…$ . These render differently: $$\sum_{i=0}^n i = \frac{n^2+n}{2}$$ (inline) or $\sum_{i=0}^n i = \frac{n^2+n}{2}\tag{displayed}$
2. For superscripts and subscripts, use ^ and _. For example, x_i^2: $$x_i^2$$.
3. By default, superscripts, subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces {…}. If you do 10^10, you will get a surprise: $$10^10$$. But 10^{10} gives what you probably wanted: $$10^{10}$$.
4. For a fraction, use \frac: \frac{a}{b} produces $$\frac{a}{b}$$; and \frac{a+1}{b+1} is $$\frac{a+1}{b+1}$$.
5. For Greek letters, use \alpha, \beta, …, \omega: $$\alpha, \beta, … \omega$$. For uppercase, use \Gamma, \Delta, …, \Omega: $$\Gamma, \Delta, …, \Omega$$.
6. Square root sign: Use \sqrt, which adjusts to the size of its argument: \sqrt{x^3} $$\sqrt{x^3}$$; \sqrt{\frac xy} $$\sqrt{\frac xy}$$. For complicated expressions, consider using {…}^{1/2} instead.
7. Parentheses Ordinary symbols ()[] make parentheses and brackets $$(2+3)[4+4]$$. These do not scale with the formula in between, so if you write (\frac12) the parentheses will be too small: $$(\frac12)$$.  Using \left(…\right) will make the sizes adjust automatically to the formula they enclose: \left(\frac12\right) is $$\left(\frac12\right)$$.
8. There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:
• \lt \gt \le \ge \neq $$\lt, \gt, \le, \ge, \neq$$.
• \times \div \pm $$\times, \div, \pm$$. \cdot is a centered dot: $$x\cdot y$$
• \cup \cap \setminus \subset \subseteq  \supset \in \notin \emptyset  $$\cup, \cap, \setminus, \subset, \subseteq ,\supset, \in, \notin, \emptyset$$
• \to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto $$\to, \rightarrow, \leftarrow, \Rightarrow, \Leftarrow, \mapsto$$
• \approx \sim \cong \equiv $$\approx, \sim , \cong, \equiv$$.
• \ldots is the dots in $$a_1, a_2, \ldots ,a_n$$ \cdots is the dots in $$a_1+a_2+\cdots+a_n$$
9. Spaces: MathJaX usually decides for itself how to space formulas, using a complex set of rules. Putting extra literal spaces into formulas will not change the amount of space MathJaX puts in.
10. To set plain text inside MathJax, use \text{…}: 3 \times 10^8 \text{meters per second} $$3 \times 10^8 \text{meters per second}$$.