If there is X, can it be reversed (made palindromic) by simply adding a character, a mathematical symbol?
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No, not a standard one. And I doubt there is even a non-standard one. It's not a common or important operation at all.
The closest concept that is commonplace is bit-reversal, an effect which actually occurs in in-place FFT algorithms. The Wikipedia page lists no standard notation for it.
The reason this operation is not so interesting is that it depends on the base in which the number is represented.
You can 'palindromize' any string of symbols, if you want--but it will take more than just one symbol addition or deletion in general.
Here is one way to palindromize a sequence. Simply take your sequence X, write it in reverse order, then concaconate X with the reversial. I.E
Your sequence: Math
Your sequence palindromized: MathhtaM. I don't know if this was what you were thinking of.