In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
Not at all. Sets have no geometrical constraints, triangles do. Most sets are not triangles, including the set you describe above. > > Like every finite initial segment of naturals has a last number every > triangle of the sequences has three limiting lines.
On certainly can think of it as a set or sequence of triangles, but a set need to be a triangle and the limit of a sequence, if it ere ro exist at all need not be the same thing as the mambers of the sequence are. For no limit of a strictly increasing sequence of naturals is natural.
WM's sloppy thinking again has lead him out of mathematics and into WMytheology. --