# MathJax basic tutorial and quick reference


Second, add \limits_{x \to 1} inside. The code now looks like $\lim \limits_{x \to 1}$, and renders as $\lim \limits_{x \to 1}$. The \to inside makes the right arrow, rendered as $\to$. The _ makes the $x \to 1$ go underneath the $\lim$. Finally, the pair of curly braces { } makes sure that $x \to 1$ is treated as a whole object, and not two separate things.

Lastly, add the function you want to apply the limit to. To make the limit mentioned above, $\lim \limits_{x \to 1} \frac{x^2-1}{x-1}$, simply use $\lim\limits_{x \to 1} \frac{x^2-1}{x-1}$.

And that is how you make a limit using MathJax.

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Why not just \lim_{x\to 1} $$\lim_{x\to 1}?$$ As I understand it \limits is only needed for operations that don't already understand limits, for example if you want to use + and get $$\mathop{+}\limits_{i=1}^k\text{ instead of }+_{i=1}^k$$ When used inline, your suggestion will produce $\lim\limits_{x\to 1}$ instead of the more compact form $\lim_{x\to 1}$ that mathjax normally chooses. Are you sure this is good advice? – MJD Feb 26 '14 at 14:10
@MJD $\lim_{x\to 1} renders to$\lim_{x\to 1}$, and $\lim\limits_{x\to 1 renders as $lim\limits_{x\to 1}$. Note how the $x\to 1$ is separated from the first limit, and not directly underneath. We do not write limits like that in real life, so we use \limits. – JChau Feb 26 '14 at 16:19
I meant that the second limit renders to $\lim \limits_{x \to 1}$ – JChau Feb 26 '14 at 16:28
Limits are usually written that way in typeset materials like papers and books when the limit is inline, rather than a displayed formula, and that's why MathJax typesets it that way. – MJD Feb 26 '14 at 16:41
The issue with this answer is that it is trying to "force" display mode on inline code. Doing so makes the text look less pretty. For example, see how the spacing between the lines change when I force display mode using \lim\limits_{x\mapsto 1}\dfrac1x: $\lim\limits_{x\mapsto 1}\dfrac1x$. On the other hand, when I let $\TeX$ do what it wants to do, using \lim_{x\mapsto 1}\frac1x, the spacing between the lines stays the same, which is much neater: $\lim_{x\mapsto 1}\frac1x$. This is much easier on the eyes. If you want to make your math mode more prominent then take a new line using $$-$$ – user1729 Jul 17 '14 at 12:30
The moral is: $\TeX$ was written by a jolly clever chap. Let it do what it wants, because it does it for a reason! – user1729 Jul 17 '14 at 12:35
Part 11 of the "question" shows how to write limits in the way they were meant to be written in LaTeX and MathJax. – David K Nov 14 at 23:17

# Absolute values and norms

The absolute value of some expression can be denoted as \lvert x\rvert or, more generally, as \left\lvert … \right\rvert. It renders as $\lvert x\rvert$.

The norm of a vector (or similar) can be denoted as \lVert v\rVert or, more generally, as \left\lVert … \right\rVert. It renders as $\lVert v\rVert$. (You may also write \left\|…\right\| instead.)

In both cases, the rendering is better than what you'd get from |x| or ||v||, which render with bars that don't descend low enough and sub-optimal spacing. At least on some browsers, so here is a screenshot how it looks for me, using Firefox 31 on OS X:

And here is the same formula rendered by your browser:

$$|x|, ||v|| \quad\longrightarrow\quad \lvert x\rvert, \lVert v\rVert$$

It was typeset as

$$|x|, ||v|| \quad\longrightarrow\quad \lvert x\rvert, \lVert v\rVert$$

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You can use \|x\| instead of \lVert x \rVert; $\|x\|$ and $\lVert x \rVert$. (I don't think that there is a difference between them. I've tried [asking on SE](tex.stackexchange.com/questions/77767/whats-the-correct-way-to-write-norm).) – Martin Sleziak Jun 24 '14 at 8:48
On my browser |x| and \lvert x\rvert ($|x|$ and $\lvert x\rvert$) look identical, contrary to your claim. Perhaps you need to show an example more complicated than just 'x'? – MJD Jun 24 '14 at 12:39
@MJD: What's your browser? I included a screenshot to support my claim. – MvG Aug 13 '14 at 11:24
Usually various versions of Firefox on either Linux or Windows. I happen to have Windows 8 booted now, so here's a screenshot from there: a.pomf.se/jrujkq.PNG The bar height looks good on both pairs of symbols; the spacing is a little off for the || version. On Linux they looked the same. – MJD Aug 13 '14 at 17:02
Here's a screenshot with FF 31.0 under Linux: a.pomf.se/fhwmjo.png – MJD Aug 16 '14 at 6:23

## Left and Right Implication Arrows

Another way to display the arrows for right and left implication instead of using

$\Rightarrow$, $\Leftarrow$ and $\Leftrightarrow$

which produces $\Rightarrow$, $\Leftarrow$ and $\Leftrightarrow$ respectively, you can use

$\implies$ for $\implies$, $\impliedby$ for $\impliedby$ and $\iff$ for $\iff$

The latter of which produces longer arrows which may be more desirable to some.

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The degree symbol for angles is not ^\circ. Although many people use this notation, the result looks quite different from the canonical degree symbol shipped with the font:

90° renders as $90°$ while 90^\circ renders as $90^\circ$.

If your keyboard doesn't have a ° key, feel free to copy from this post here, or follow these suggestions.

Note that comments below indicate that on some configurations at least, ° renders inferior to ^\circ. And I recently had a post of mine edited just for the sake of turning ° into ^\circ, indicating that someone felt rather strongly about this. So the suggestion above does seem somewhat controversial at the moment. I maintain that from a semantic point of view, ° is superior to ^\circ, and if the rendering suffers from this, then it's a bug in MathJax. After all, LaTeX offers a proper degree symbol in the tex companion fonts, indicating that someone there, too, decided that ^\circ is not perfect. But if things are broken now, I can't fault people from pragmatically sticking with the rendering they prefer. Personally I prefer semantics, also for the sake of screen readers.

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If mathjax loads siunitx or gensymb, there is then \degree in latex which is the degree symbol. – dustin Feb 17 at 22:29
@dustin: I couldn't find siunitx or gensymb mentioned anywhere in the MatJax source repository. Are they available as some kind of third-party extension? If so, where? Since MathJax is not LaTeX, packages can't be loaded unless they have been migrated. By the way, all occurrences of “degree” in the MathJax sources refer to something else, as far as I can tell, so there really doesn't seem to be a \degree macro. There should be one, imho. – MvG Feb 17 at 23:39
I am not a mathjax expert. I just know latex. I just gave that suggestion in case they were available. Siunitx would be a great package to have. If you aren't familiar, you will see the advantage by scanning the documentation on ctan. – dustin Feb 17 at 23:43
On my display, ° looks bad and ^\circ looks good: a.pomf.se/xnlfyg.png – MJD Mar 24 at 21:10

## Long division

$$\require{enclose} \begin{array}{r} 13 \\[-3pt] 4 \enclose{longdiv}{52} \\[-3pt] \underline{4}\phantom{2} \\[-3pt] 12 \\[-3pt] \underline{12} \end{array}$$


$$\require{enclose} \begin{array}{r} 13 \\[-3pt] 4 \enclose{longdiv}{52} \\[-3pt] \underline{4}\phantom{2} \\[-3pt] 12 \\[-3pt] \underline{12} \end{array}$$

One important trick shown here is the use of \phantom{2} to make a blank space that is the same size and shape as the digit 2 just above it.

This is adapted from http://stackoverflow.com/a/22871404/3466415 (which uses slightly different but not less valid formatting).

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## Giving reasons on each line of a sequence of equations

To produce this: \begin{align} v + w & = 0 &\text{Given} \tag 1\\ -w & = -w + 0 & \text{additive identity} \tag 2\\ -w + 0 & = -w + (v + w) & \text{equations $(1)$ and $(2)$} \end{align}

write this:

\begin{align}
v + w & = 0  &\text{Given} \tag 1\\
-w & = -w + 0 & \text{additive identity} \tag 2\\
-w + 0 & = -w + (v + w) & \text{equations $(1)$ and $(2)$}
\end{align}

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## protected by MJDMay 28 at 17:18

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