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In order to center stuff in math mode, we can use either $$...$$ or \[...\]. Is there an OBJECTIVE reason as to why one is better than the other?

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From the l2tabu document (section 1.6):

1.6 Separating maths formulae from continuous text using $$...$$

Please don’t do this! $$...$$ is a Plain TEX command. It will modify vertical spacing within formulae, rendering them inconsistent. This is why it should be avoided in LATEX (see section 3.3 on page 15; note the warning concerning displaymath along with the amsmath.sty package). What’s more, class option fleqn won’t work any more. Replace: $$...$$ by \[...\]

or

\begin{displaymath}

...

\end{displaymath}

So assuming you consider a preference for consistency objectively justified, yes, there is an objective reason to use one rather than the other.

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  • OK, thanks. One question though, what does it mean by "It will modify vertical spacing within formulae"? – Mathematician Jun 25 '14 at 1:42
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    @Mathematician See tex.stackexchange.com/a/69854/39222 which is much better than the top rated answer to the original of your question. (And much better than my semi-answer here.) – cfr Jun 25 '14 at 2:21

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