On 10 Apr., 22:56, Virgil <vir...@ligriv.com> wrote: > In article > <ec790c67-8252-4cc4-97b7-30bf73d22...@t5g2000vbm.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > 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. > > Claiming what you are trying to prove does not constitute a proof of > what you are trying to prove.
*There are* infinitely many rational numbers the decimal representation of which begins with d _1, d_2, d_3, ..., d_n. At least if infinity is considered a meaningful notion.