On 12 Okt., 01:53, Virgil <vir...@ligriv.com> wrote: > In article > <940ad68c-0ab6-4776-a4d7-7cfd6b2dd...@c28g2000vbz.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 11 Okt., 21:18, Virgil <vir...@ligriv.com> wrote: > > > In article > > > <cd7d85c0-2a79-4bbe-83ca-d1af58ce0...@dd6g2000vbb.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 11 Okt., 03:02, William Hughes <wpihug...@gmail.com> wrote: > > > > > On Oct 10, 12:52 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 10 Okt., 16:04, Alen <al...@westserv.net.au> wrote: > > > > > > <snip> > > > > > > > o > > > > > > oo > > > > > > ooo > > > > > > ... > > > > > > > with aleph_0 lines but less than aleph_0 columns, because there is no > > > > > > natural number made of aleph_0 circles. > > > > > > Sigh! The number of columns is the supremum of the line length. > > > > > This supremum > > > > > is aleph_0 despite the fact that there is no natural number made of > > > > > aleph_0 > > > > > circles. number of lines = number of columns = aleph_0 > > > > > Agreed. But then infinity is also not realized in the diagonal. > > > > Having just conceded that it IS realized in both the rows and columns? > > > If actual infinity with aleph_0 circles is in fact realized (not only > > being the supremum) in both the rows and columns, then the triangle > > has equal height and width = aleph_0 circles. Its width cannot be > > larger than every line. Therefore there must be a line with aleph_0 > > circles. Contradiction. > > Actually its width MUST be larger than every line
But its width is spanned by the lines. There is nothing more.
> or it would have to be > equal to some line,
only if infinity was finished. Result: actual infinity requires something beyond all natural numbers. Contradiction.
