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But F(pi) + F(0) depends on n, rather than being a number, just this isn't explicitly spelled out. So all the proof shows is that the integral (1) converges to
by rich_sasha 2y ago
But F(pi) + F(0) depends on n, rather than being a number, just this isn't explicitly spelled out. So all the proof shows is that the integral (1) converges to 0 rather quickly, as a function of n.
The claim of the proof is that I=F(0)+F(π) is simultaneously positive and arbitrarily small, which is not possible for a fixed number, but totally possible if you see I as a sequence indexed by n.
- alimw 2y ago> The claim of the proof is that I=F(0)+F(π) is simultaneously positive and arbitrarily small, which is not possible for a fixed number, but totally possible if you see I as a sequence indexed by n. This is not possible because I_n must be an integer for every n.
- rich_sasha 2y agoAh yes, that's the key bit. Thanks!