Comment by nmrm | Hacker News Reader

Comment by nmrm | Hacker News Reader

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I have a feeling that the problem is students show "If the equation is true, then 0=0" instead of "Note that 1=1; now, we derive P".

Even if all facts used in the proof are true "in both directions", it's still a serious breach of modern mathematical style to start with what you're trying to prove.

It's also possible that they don't explicitly note that the facts they're using are "true in both directions". edit: to be explicit, in that case I'd still consider the proof wrong

Anyways, if a student presented a proof like that, I would at least take a couple points off for the awkward style unless it was explicitly justified somehow.

It's also kind of a weird proof technique to start with 0=0 or 1=1 and bother to explicitly state this fact...

From reading math research papers, it is not that uncommon to start with what you are trying to prove and proceed with a series of reverisible operations. This is gennerally done to as a first step to convert the proposistion into something that fits more naturally into the proof. This also tends to be done in prose.

It saddens me that so little of what goes in in math papers makes it into textbooks, or math students that do not study original papers themselves.

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.

Like I said above, induction can be used to prove facts which are not equations. In fact most equations are best proved without induction, at least in my opinion. I was getting this argument even when the fact to be proved was not an equation, it is an affirming the consequent fallacy.

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