I found from http://jblevins.org/notes/latex that I could use the independence symbol:

`\newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}} \def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}`

I was wondering how this works. Can anybody explain? I don't know the commands `mathpalette`

, `rlap`

, and `mkern2mu`

.

## Best Answer

`\mathpalette`

: See The mysteries of`\mathpalette`

.`\rlap`

: This is referred to as a`r`

ight over`lap`

. That is, it makes a box of width`0pt`

, and aligns the contents within to the left, similar to`\makebox[0pt][l]{<stuff>}`

, causing the contents to overlap to the right.`\mkern`

: Kerning (or spacing) in math mode. The unit of measure is`mu`

(or`m`

ath`u`

nits). So,`\mkern2mu`

inserts a kern or space of`2mu`

horizontally. For a take on these lengths (and others), see What are the possible dimensions / sizes / units LaTeX understands?Specific to your question about how this works:

The use of

`\mathpalette`

- defined internally as a specialized`\mathchoice`

- allows the input to do defined in a way that captures the current math style. Note that there are four different math styles:`\displaystyle`

,`\textstyle`

,`\scriptstyle`

and`\scriptscriptstyle`

.The above MWE shows how the single command

`\independent`

scales to regardless of where it's used, all because of a nifty use of`\mathpalette`

and a helper macro`\independenT`

. The helper macro captures the current math style and re-uses it inside an`\rlap`

. The double use of the symbol is just for spacing purposes, adding to the`\mkern`

insertion. That is, it sets the symbol`\perp`

(of width`0pt`

and`r`

ight over`lap`

), inserts of`2mu`

kern (pushing the "cursor" to the right`2mu`

s) and then inserts the symbol again. Since the symbol is set in the same style, the horizontal bar overlaps, but the vertical bar is spaced`2mu`

apart. As a final take on mathematical spacing, the entire symbol is set as a relation using`\mathrel`

.