On 11 Apr., 10:37, Virgil <vir...@ligriv.com> wrote:
> > > > 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. > > Claiming what you are trying to prove, which is exactly what you have > done above, STILL does not constitute a proof of what you are trying to > prove.
I do not claim to prove this self-evident truth. I expect that every hominid knows it. If you don't then wait a while and think about it. It cannot be exculded that you will understand sometime.