In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 6 Dez., 11:36, Virgil <vir...@ligriv.com> wrote: > > In article > > <fb9f656b-8ae6-4e38-87d1-33e24c7d9...@a2g2000yqh.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 6 Dez., 10:36, Virgil <vir...@ligriv.com> wrote: > > > > In article > > > > <cc5c24a4-0ec4-4f48-8b90-9463aed1b...@o6g2000yql.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 5 Dez., 19:48, Virgil <vir...@ligriv.com> wrote: > > > > > > > > WM has already adequately demonstrated to the world again and again > > > > > > that > > > > > > he does not speak for mathematicians > > > > > > > Is aleph_0 a quantity (i.e. possibly in trichotomy with other > > > > > quantities) or not? > > > > > > Not to those who, as in the case of WM, deny that it can be properly > > > > defined as a cardinality or ordinality. > > > > > > But not everyone is so negatively oriented towards such things as > > > > general definitions of cardinality and ordinality as WM is. > > > > -- > > > > > So, to you it is a quantity? Then we can put the question whether the > > > lengths of the sides of my triangle can be in trichotomy. There is an > > > angle of 45 and its sides have length 1*aleph_0 = aleph_0 and > > > sqrt(2)*aleph_0 = aleph_0. Now my question: Is the third side aleph_0 > > > or less or larger? > > > > Until you can show that those alleged "sides" have endpoints other that > > that alleged common point, you question assumes conditions contrary to > > fact. > > I can show that the endpoints are closer to the common point than the > unit length time 2^aleph_0.
Actually, you cannot, or at least have not, shown that they exist at all.
A part of your argument seems to be that endless sequences must have two ends, which is sufficiently contrary minded to be mathematically unacceptable.
> If we can surpass them, walking along the > sides of the angle, they must be somewhere.
If you could 'surpass' them, they would not be endless sequences, which you have already claimed them to be. --