One caveat, though: \middle, unlike \mid, will not automatically insert any space around the vertical bar that's left to the user. Notice that the positions depend only on the direction of the arrow, the absolute notions of up, down, etc. For more on \mid and \middle, you may want to check out the TeX FAQ topic Set specifications and Dirac brackets. ized as sub- and superscripts on arrows such that they are placed in the usual positions (as limits), i.e., reads above and below on an arrow pointing right. I.e., something like \middle| will work on most systems that are based on eTeX or one of its descendants. This omission is addressed in eTeX ("Extended TeX") and successors such as pdfTeX. There is actually no \middle construct in the orginal TeX engine. If you want larger versions of the vertical bar as a relational symbol, while preserving the nice spacing on either side, you can write \bigm|, \Bigm|, \biggm|, and \Biggm|. being greater than 0 as $\mathrm(\,X\ |\ X>0\,)$ because \ inserts a "thick space". For instance, if X is a random variable, one might denote its expectation conditional on the r.v. A good use of this symbol, for example, is when one needs to denote the fact that the material to the left of the vertical bar is being conditioned on what's to the right of the vertical bar. The instruction \mid (in math mode, of course), produces a vertical bar with a "thick space" on either side. I can tell you something about the use of \mid, though. \divides once again produces the same symbol but should be used as a binary divides operator. \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). I can't claim to possess any special insights into Don Knuth's linguistic preferences. \mvert and \mid are identical and produce a relation.
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