Spacing around \left and \right: When is it needed? [closed]

There have been a few questions (such as this and more recently this) regarding the "extra" spacing around \left and \right. And there are various options for fixing it, including the mleftright package. Is there any time we would actually want the default behavior? Is there any situation in which redefining \left and \right to get rid of the space would produce an inferior result?

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closed as not constructive by Stephan Lehmke, Kurt, Paul Gaborit, Guido, ThorstenDec 2 '12 at 7:09

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I'm not sure this is really an answerable question in this form. Clearly someone preferred this behaviour as it is not an accidental side effect in the code of TeX, the whole mathinner node type is introduced to produce this effect. Personally I think it works out OK when the delimiters are being used around matrices or large subterms generally. It works a lot less well in conjunction with a mathop where you have a prefix function name nut need big brackets. – David Carlisle Nov 15 '12 at 21:15
I like this question a lot, and was thinking about asking it myself; I was wondering what the consequences of trying something like \left\left\mleft... – cmhughes Nov 15 '12 at 22:25
opps, I meant to say \let\left\mleft – cmhughes Nov 15 '12 at 23:49
See The TeX Book, p.155 : "There's also an eighth classification, \mathinner, which is not normally used for individual symbols; fractions and \left...\right constructions are treated as "inner" subformulas, which means that they will be surrounded by additional space in certain circumstances." – Thruston Nov 28 '12 at 10:16
And as the preceding paragraph on the page makes clear, if you want to treat it differently you can do by using one of the \mathxxxx primitives to change it into a different math atom. In the particular case referred to in the above questions all that is needed is to do something like $\cos\mathopen{\left(\theta\right)}$, which turns the \left(\theta\right) part into a mathopen atom instead of a mathinner and because ( is normally defined as a mathopen atom, this produces the same spacing as an unadorned \cos(\theta). – Thruston Nov 28 '12 at 10:23