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Well, it's a proof as long as you stipulate somewhere that all the logical connectives are "if and only if." This doesn't mean that a student who writes down a
by aesthesia 6y ago
Well, it's a proof as long as you stipulate somewhere that all the logical connectives are "if and only if." This doesn't mean that a student who writes down a long series of equations beginning with some identity to be proven and ending with some known fact has proven the identity.
- voxl 6y agoSure, that's fine, but to say that it is an invalid method of proof is wrong. If I want to prove A, and I prove A <=> B for some proven statement B, then I have proven A! There is no question! Feels like crazy pills to think otherwise. This is a kind of backwards reasoning!
- grayclhn 6y agoIt is a kind of backwards reasoning that students empirically screw up all the time. Edit: so much so, that I would definitely recommend students rewrite these proofs on assignments as an exerecise to make sure it's correct. By the time they reach a math PhD they probably don't need to do that anyomre. :)