Help:FAQ/Questions about contributions/Why do we need \left and \right with every pair of parentheses?

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Why do we need \left and \right with every pair of parentheses?

"Do we really need to put \left({ ... }\right) for every parenthesis, even things like $\sin(2x)$ and $(2n)!$? Out of curiosity, what difference does the extra curly inside \left(...\right) make? It seems to display the same."

The curly braces are grouping indications for $\TeX$; they serve to ensure that every \left is paired with the intended \right. Especially when using an external editor (e.g. via the Firefox plug-in It's all text) that highlights matching braces, such can greatly simplify the frustrating search for an occasional omitted or excess brace.
We enforce it to avoid problems with copy-pasting and subsequent editing of stuff inside parentheses. In this way, the parentheses will always size appropriate to their content, even if that content vertically grows or shrinks due to changes.
Equation references like $(1)$ and $(3′)$ are excepted from this admittedly strict style rule. --Lord_Farin (talk) 17:57, 13 December 2012 (UTC)
UPDATE: This has now been more or less superseded by the new custom $\LaTeX$ commands which have recently been added. Please consult Symbols:LaTeX Commands/ProofWiki Specific for an idea of the sort of thing we are moving towards, for example: $\map f x$ is now generated using \map f x, and $\tuple {a, b, c}$ by \tuple {a, b, c}, and so on.