3. Re: An irrational number normal to every radix simultaneously (Andy Latto)

--Andy, your random number algorithm works, but only with probability 1. But the FACT that it works with prob=1 proves EXISTENCE of many normal numbers, and finite versions of same existence proof prove existence of finite chunks that are used by my algorithm to add a new chunk at a time. It was that sort of existence argument I had in mind to fill (what you complained was a gap, lack of proof) to create a genuine proof. The function F(N) had to grow slowly enough, but it seemed clear to me that if it did such a proof would exist. (Sort of, in the "limit" of "very slow growth" of F, we get the continuum limit which Andy Latto had in mind for his random bit algorithm -- which makes it "obvious" that this attack must work.) Turing also had a proof apparently of this vague ilk in mind, though I have not attempted to read or confirm his details. It might be interesting if ways can be found to make some version of this slick and efficient.