8 Dec
2018
8 Dec
'18
5:32 p.m.
Hmm, so consider the analytic function f(z) = Sum_{0 <= n < oo} z^(2^n) which converges only on the open disk |z| < 1. Is it true that f takes rational numbers in (-1, 1) to transcendentals? —Dan Keith Lynch wrote: ----- ... So 1/2 + 1/4 + 1/16 + 1/256 + 1/65536 + ... is not a greedy sequence. Still, I wonder whether its sum has any significance. Similarly with other starting points, e.g. 1/3 + 1/9 + 1/81 + 1/6561 ... -----