Here's a solution that doesn't require the use of additional packages. The new command, \vertiii, takes one argument; the triple vertical bars resize automatically depending on the size of the argument. For the MWE below, I've actually set the spacing between the vertical bars to be slightly less than what's generated by [l,r]Vert -- you can adjust the spacing to suit your taste by changing ...
You cannot, \mid is not a fence it is a binary symbol. I would also suggest making a macro for sets and thus hide the vertical line inside the macro. Then it is also easier to change syntax later on instead of having to do a lot of search and replace. (personally I tend to use mathtools to build such a set macro).
According to texdoc symbols: \mvert and \mid are identical and produce a relation. \vert is a synonym for | and both produce the same symbol, but should be used in the context of an ordinal, and should be used as an operator, not as a delimiter (p54, bottom). \divides once again produces the same symbol but should be used as a binary “divides” operator. \lvert and \rvert are left and right ...
As you can see, the top formula has \vert size as default. I want the latter formula, How do I change my command? I can't use the \left and \right command because there is no left or right in \vert. Any help is appreciated.
How can I change the size of \vert accordingly like \left and ... - TeX
In short, \bigl\vert