User talk:Kiyura/Mathematical Proof

As you can see, I have removed many sections. I think most of them were beyond the scope of the article. The concept of a mathematical proof applies to virtually every branch of pure mathematics, so to cover all major proof methods and all notable instances of proofs only makes it cluttered and unfocused (as it certainly was).

This current revision, in my opinion, makes the article read better. I have eliminated the “Methods of proof” section in favor of three major sections: 3) Direct proof, 4) Proof by contrapositive, and 5) Proof by contradiction. I feel that these three give an adequate sampling of logical techniques used to prove, and that all major methods of proof can be allocated to one of the three - primarily direct proof. The actual content of these sections (and some others below them) could still do with some addition and revision.

Sections 6-10 are still somewhat cluttered, and could do with some further culling and organization. I’d rather have further input on that, if anyone else has the skill and interest. I would want to do away with sections 6, 9.3, 9.4, and 9.5. I would also want to create a new section right after “Nature and purpose”, called “Structure of a proof” or simply “Structure”. It would cover the basic outline of a proof, give one or two examples, and segue into the definition of a direct proof. Section 10 could also be merged into that “Structure” section.

So, if you have the interest and time, please give your opinion on these suggestions as well as the revisions I have already made. Please see the page history to review them - most of the removals and reorganization are in the last edit. Kiyura (talk) 20:08, 23 May 2009 (UTC)

We could probably use this image for an example of proof complexity based on audience: File:IdempotentCosineAngle.jpg. It's a visual proof that there is an angle t such that cos(t)=t, reproduced from the Solow text sourced in the article. Kiyura (talk) 20:49, 23 May 2009 (UTC)

I like your revision overall, though I'm not sure about giving an entire section over to Proof by Contrapositive, since I would put this as a technique of Direct Proof (especially since it's only one sentence long). On the other hand, Proof by Induction is an important method of proof, used in all areas of mathematics, and quite different to other types of proof, so I'd suggest that this have its own section. --Joth (talk) 09:26, 1 June 2009 (UTC)