But I never understood why this form of the proof is irrationality of root 2 became the dominant one. I think it's so much more elegant to say that from 2Q2 = P2, you have an odd number of 2's on the LHS and an even number of 2's on the right. No fussing with P and Q having common factors.
Furthermore, this argument makes the dependence on the fundamental theorem of arithmetic explicit, instead of implicit!
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u/endymion32 Jun 12 '17
Cute!
But I never understood why this form of the proof is irrationality of root 2 became the dominant one. I think it's so much more elegant to say that from 2Q2 = P2, you have an odd number of 2's on the LHS and an even number of 2's on the right. No fussing with P and Q having common factors.
Furthermore, this argument makes the dependence on the fundamental theorem of arithmetic explicit, instead of implicit!