I don't see any pressing need to freshman to write their very first non-euclidean proofs in the same style as professional mathematicians. Obviously, it's a ma

I don't see any pressing need to freshman to write their very first non-euclidean proofs in the same style as professional mathematicians. Obviously, it's a matter of style. I still maintain few mathematicians would write canonical discrete math style induction proofs in reverse order. But then, a mathematician would totally not write out induction proofs the same way we teach in freshman discrete math courses. So in some sense the style question is completely irrelevant, and what matters is that the student's answer demonstrates unambiguously an understaning of the concept.