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The typical formulations of all of those proofs are by contradiction, though—so it may be worth distinguishing “prove” from “demonstrate by proof”.
by evincarofautumn 14y ago
The typical formulations of all of those proofs are by contradiction, though—so it may be worth distinguishing “prove” from “demonstrate by proof”.
- alanctgardner2 14y agoIs 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.