On 10 Apr., 08:59, William Hughes <wpihug...@gmail.com> wrote:
> Next argument.-
Consider a Cantor-list that contains a complete sequence (q_k) of all rational numbers q_k. The first n digits of the anti-diagonal d are d_1, d_2, d_3, ..., d_n. It can be shown for every n that the Cantor- list beyond line n contains infinitely many rational numbers q_k that have the same sequence of first n digits as the anti-diagonal d. Proof: There are infinitely many rationals q_k with this property. All are in the list by definition. At most n of them are in the first n lines of the list. Infinitely many must exist in the remaining part of the list. So we have obtained: For all n exists k: d_1, d_2, d_3, ..., d_n = q_k1, q_k2, q_k3, ..., q_kn
Every property that holds for all FISs d_1, d_2, d_3, ..., d_n of d, also holds for all digits d_n of d that can be subject to digit- reversal and digit comparison.