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May 14, 2014 at 3:27 comment added Sridhar Ramesh Oh, very nice, thank you. This does settle the question about the existence of the general limit, but, alas, this argument requires that we already know $\prod_{p}(1 - 1/p) = 0$, while my motivating hope remains that there is some way to noncircularly derive this fact from $\prod_{p}(1 - 1/p) = \lim_{q \to \infty} \lim_{n \to \infty} f(n, q)^{-1}$ and $\lim_{n \to \infty}\lim_{q \to \infty} f(n, q)^{-1} = 0$.
May 14, 2014 at 0:39 history edited so-called friend Don CC BY-SA 3.0
typos corrected
May 14, 2014 at 0:34 history answered so-called friend Don CC BY-SA 3.0