In the past we had a couple of discussions, and it was decided -- I thought -- that the tag proof shouldn't be used. Now we have more than 50 questions with this tag again. Could we please get it merged with make it synonym of [tag-removed]? (Or disable it in some other way.)

Mathematicians typically define rational number to mean quotient of two integers. It is not hard to show that a number is rational by that definition if and only if its decimal expansion terminates or repeats. Let us call that the “decimal characterization” of rationality. The proof of that char...