On 13 Feb., 19:00, William Hughes <wpihug...@gmail.com> wrote: > On Feb 13, 8:54 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 12 Feb., 20:40, William Hughes <wpihug...@gmail.com> wrote: > > > Your first claim is that there is a line l such that > > > d and l are equal as potentially infinite sequences. > > > For every n this is true. > > Your other claim is that there is no line > l such that d and l are equal as potentially infinite > sequences. > > Do you deny you have claimed this?
No, of course not! Why should I do so? You cannot discern that two potentially infinity sequences are equal. When will you understand that such a result requires completeness? But potentially infinite sequences are not complete. You can only *for every n* determine whether identity is true.
*And that is true in the list!* For every n there is a FIS of d and a line l such that both are identical. This follows from the undisputed fact that the diagonal cannot stretch farther than any line.
Here is no complete list, no complete diagonal and no line containing a complete diagonal.
1 12 123 ...
But for every n the FIS(n) of d is in line(n). That is all we can know about infinite lists.