I use \arrowvert as a middle delimiter. For example in the definition of sets, i.e. \lbrace x \arrowvert x < a \rbrace. Moreover, I try to avoid \left, \right and \middle but use the AMSmath macros \bigl, \Bigl, ... to set the size explicitly.
If I need the delimiters in "normal" size, I do not use any macro, but then I notice a different horizontal (!) spacing. Consider the case in that \left, \right and \middle can be used without effect, because all enclosed symbols have at most normal size. Then
\lbrace x \arrowvert x < a \rbrace
\left\lbrace x \middle\arrowvert x < a \right\rbrace
look the same vertically, but there is a little bit more horizontal space of both sides of the middle delimiter. Actually, the visual appearance of the latter looks more correct.
The same amount of additional space around the middle delimiter is inserted by the AMSmath keywords \big, \Big, ...
But what shall I do, if I need the normally sized delimiters but cannot use the triplet \left, \middle, \right because there is some over-sized content?
Using no macro as suggested by the AMSmath manual is no option, because then the additional space around the middle delimter is missing. Unfortunately, there does not seem to be something like a \normall, \normal, \normalr triplet that does no scaling but fits the horizontal spacing of the other macros.
\middo what you want? (in normally sized) – morbusg Nov 11 '14 at 10:31\midis a binary operator and has a totally different spacing. Actually one should never use\midin this context because it has the wrong class-code. But even if one would not care of correct class-codes and only consider correct visual appearance,\midlooks totally different.\arrowvert,\vert,\bracevertand just|are all (middle) delimiters (with different "thickness"). I can see this slight different behaviour with all of them. – nagmat84 Nov 11 '14 at 10:39mathtools, in particular to\DeclarePairedDelimiterX– egreg Nov 11 '14 at 11:03\mid, which is a relation symbol, so it's the right kind. The difference is that\arrowvertis arbitrarily extendable, which\midisn't; but\midhas rounded ends, while\arrowverthas sharp ends. – egreg Nov 11 '14 at 12:35