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aaronhotchner wrote:
Black Swan wrote:Are you sure? I mean, I’m not a math expert, but I feel like I’ve canceled (X+1)*X = (X+1) for a result of X=1 or similar equations many a time.
I’m positive. (X + 1) * X = (X + 1) implies X^2 + X = X + 1 which implies X^2 = 1. There are actually two solutions: X = -1 or X = 1, and by cancelling you completely ignored one of them. The same applies to your proof: it just assumes away possibilities that you aren’t allowed to do with deductive reasoning.
Actually, I solved the simplification incorrectly in that example (it is +-1, but I’m sure that arithmetically it’s correct now that you’ve said that. And that proves that you can in fact cancel that term when the outside term is a constant.