Re:The Most Common Errors in Undergraduate Mathematics (2009)
by aesthesia on Thursday November 19, 2020 @12:06PM
(#25151568)
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.
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Re:The Most Common Errors in Undergraduate Mathematics (2009)
by voxl on Thursday November 19, 2020 @12:55PM
(#25152191)
Sure, 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!
Re:The Most Common Errors in Undergraduate Mathematics (2009)
by grayclhn on Thursday November 19, 2020 @03:24PM
(#25153924)
It 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. :)