For question in Proof Theory, where "proofs" themselves are the object of mathematical investigation. It is not to be used to request a proof of some result.

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55
votes
29answers
6k views

Can infinity shorten proofs a lot?

I've just been asked for a good example of a situation in maths where using infinity can greatly shorten an argument. The person who wants the example wants it as part of a presentation to the general ...
6
votes
4answers
2k views

Discharging assumptions

When constructing proofs using natural deduction what does it mean to say that an assumption or premise is discharged? In what circumstances would I want to, or need to, use such a mechanism? The ...
62
votes
16answers
5k views

When are two proofs of the same theorem really different proofs

Many well-known theorems have lots of "different" proofs. Often new proofs of a theorem arise surprisingly from other branches of mathematics than the theorem itself. When are two proofs really the ...