On 4 Dez., 10:04, Virgil <vir...@ligriv.com> wrote: > In article > <d9d8e2b0-0bda-4a42-a057-c4caa47c3...@r14g2000vbd.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > Matheology 170 > > > The infinite triangle formed by the sequence > > > 0.1 > > 0.11 > > 0.111 > > ... > > > has height aleph_0 but width less than aleph_0 (because the limit 1/9, > > the first line with aleph_0 digits, does not belong to the triangle). > > This lack of symmetry is disturbing for a physicist. > > In order to be a mathematically valid triangle, your figure would have > to have a last line, which means that you must be claiming that there is > a largest natural number corresponding to that last line, which is not > only disturbing to real physicists but also to real mathematicians.
Your objection is tantamount to requiring: In order be a mathematically valid set, the natural numbers would have to have a last number.
Like every finite initial segment of naturals has a last number every triangle of the sequences has three limiting lines.