Can someone with the book ready to hand explain how he proves the converse? He just says taking , we thus find a sequence......

Sometimes he's a little too presuming of the reader's perception.

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- Oct 17th 2011, 12:41 PMboromirTheorem 4.2 in Rudin POMA
Can someone with the book ready to hand explain how he proves the converse? He just says taking , we thus find a sequence......

Sometimes he's a little too presuming of the reader's perception. - Oct 17th 2011, 12:55 PMgirdavRe: Theorem 4.2 in Rudin POMA
Thanks to this choice, we can find a sequence such that and , hence we have shown that we don't have the part after the "if and only if".

- Oct 17th 2011, 12:58 PMPlatoRe: Theorem 4.2 in Rudin POMA
- Oct 17th 2011, 01:10 PMboromirRe: Theorem 4.2 in Rudin POMA
I think you mean q instead of F(p). So essentialy that is chosen since 1/n-> 0 (allowing x_n to be arbitarily close to 0) and x_n consists of all 'rogue' values of x is so far as they make F(x) more than epsilon away from q. Is this correct?

- Oct 17th 2011, 01:16 PMPlatoRe: Theorem 4.2 in Rudin POMA