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My friends told me that the sophisticated way to use display math in LaTeX is \[ instead of $$. Reading about the issue here on tex.stackexchange and in the l2tabu, it seems like the consensus reason why is that $$ is a TeX primitive, and thus deprecated at least since 1994 (the year I was born) with the release of LaTeX2e. Meanwhile, \[ is part of LaTeX, not TeX, so using it doesn't muck around too much in the source, it's easier to detect errors when using it, the vertical spacing is better, and it works really well with the amsmath package. (Although it does have the slight disadvantage that it is not supported by MathJax.)
My question: To what extent does all of this reasoning carry over to the decision to use either $ or \( for inline math?
The single dollar sign $ is also a TeX primitive, so seemingly it should also be deprecated for the same reason the double dollar sign $$ is.
This blog post supports the position that \( should be used instead of $, in spite of the author of l2tabu's assertion to the contrary.
However, this web page only mentions facilitating error correction and detection as an advantage of \( over $.
Who is right?