In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 4 Dez., 22:30, Virgil <vir...@ligriv.com> wrote: > > In article > > <0aa8193b-9fae-4fdf-83a8-4bc68e25e...@m13g2000vbd.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> 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. > > This set has, like many mathematical entities, a geometrical and an > alytical property: > > 0.1 > 0.11 > 0.111 > ... > It is a triangle and it is a sequence too.
While parts of it can be triangular by reason of having 3 finite sides, the whole of it does not have a third finite side so is not a triangle.
NOte that to be a triangle, it would also have to have three vertices, which is not the case.
> > > > > 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 > > But in case of the set above the terms of the sequence are rational > numbers and the limit 1/9, which is not in the sequence, is a rational > number too. So wie have aleph_0 lines but never aleph_0 digits 1 in > one line.
Even if it were true that 1/9 were a line, which it isn't. rather than merely a rational number, since 1/9 does not have any endpoints, WM still does not have a triangle, at least not anywhere outside his Wolkenmuekenheim. > > My construction does nothing else but to cover every 1 in an > alternative way. Nothing more nothing less. My construction shows that > there is never a completed infinity aleph_0, neither in the width nor > in the height.
WM's constructions almost never display the mathematical properties he reads out of them, and certainly do not here. > > > WM's sloppy thinking > > Sloppy thinking is not to distinguish between actual and potential > infinity like matheologians do here and on many other occasions.
One can easily distinguish between them. The actual ones occur in standard mathematics, as in the sets of naturals, integers, rationals and reals, among other places, and WM's potential ones only in his WMatheology. --