Is there a distinction between proving and demonstrating by proof? I did a quick search (I'm hardly a mathematician), to quote Wikipedia:
> a proof must demonstrate that a statement is always true
It would seem that, if you can demonstrate a statement is true for a given logic, that is proof. Contradiction and exhaustion (which is a bit more controversial, I think), while less tidy than one might expect, are valid techniques for showing that a statement is always true, and therefore are valid ways to construct a proof.
Note: I encourage any and all maths professors to come and tell me off if I'm way off base.
> a proof must demonstrate that a statement is always true
It would seem that, if you can demonstrate a statement is true for a given logic, that is proof. Contradiction and exhaustion (which is a bit more controversial, I think), while less tidy than one might expect, are valid techniques for showing that a statement is always true, and therefore are valid ways to construct a proof.
Note: I encourage any and all maths professors to come and tell me off if I'm way off base.