Now I use "mid" for all vertical bars, but I wonder what's the proper ways.

The first scenario is vertical bar for absolute value. Now I just right `$x\leq \mid x \mid$`

. but is this correct?

The second scenario is in conditional expectation. Now I write `E[x \mid y]`

, but sometimes if the "x" part is complex, it might be quite "tall", I wonder if there's a way to have a "automatically adjusted" vertical bar. Is there?

## Best Answer

As others have remarked, vertical bars can be obtained with different commands and one should use the correct one in each case:

`\mid`

when it's a relation symbol, for instance in set notation or for “divides”;`\lvert`

or`\rvert`

when it's a (left or right) delimiter; note that this requires`amsmath`

that's recommended anyway when a document needs math.Just typing

`|`

can work, but there are some subtleties, so it's better to use the above commands. Similarly, for the double bar is`\parallel`

when it's a relation symbol;`\lVert`

or`\rVert`

when it's a delimiter.You can exploit

`mathtools`

for your symbol for expectation, but with some more tricks in order to make the bar doing the right thing.In the same style as macros declared with

`\DeclaredPairedDelimiter`

, you can give`\expect`

an optional argument that can be one among`\big`

,`\Big`

,`\bigg`

or`\Bigg`

for manually sizing the delimiters or use`\expect*`

in order to get automatic sizing (use it sparingly).Here you

canuse`|`

for conditional expectation, because the macros take care of its relation nature.## UPDATE

A revamped definition that uses new features of

`expl3`

and`xparse`

. This also allows to specify the measure of the expectation.