Regardless of the purpose, I wonder whether one can redefine $$ by \[ ... \]?
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If \(...\) is close enough this there is great detail in the answers here:
Are \( and \) preferable to dollar signs for math mode?
$$forms part of\[and\]. Any reason why you want this? – Werner Jun 25 '15 at 04:36$$maths$$with\[maths\]using regex. If that is your question then I'll make an answer explaining it! – Paul Stiverson Jun 25 '15 at 04:54