As far as I know, by default they're all defined to be the same bar, except for maybe some spacing differences. But LaTeX, like properly written HTML, favors semantic markup over purely functional markup - you use the command for what you mean, rather than just what you want to appear on the page. This way, if you decide later on that you want certain kinds of bars to look different, it's easier to change only the bars you actually want to and not mess with anything else. For example, if you want to have less space between the bars and the text in constructions like |x|
, you can redefine \lvert
and \rvert
appropriately.
As qbi said, it is recommended to define a higher level of semantic markup, namely things like \abs
, \norm
, \union
, \or
, \suchthat
, etc., to represent what you really mean in your formulas, and to use those instead of \vert
, \lvert
and \rvert
directly.
|
does not have.