On 27 Nov., 08:41, Virgil <Vir...@home.esc> wrote: > In article > <aa9e46c0-56da-4510-8345-8dee84745...@b2g2000yqi.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 27 Nov., 02:50, William Hughes <wpihug...@hotmail.com> wrote: > > > On Nov 26, 4:51 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 26 Nov., 19:22, William Hughes <wpihug...@hotmail.com> wrote: > > > > > Only in Wolkenmuekenheim. Outside of Wolkenmuekenheim > > > > > you will have an empty set. > > > > > Besides your assertion, you have arguments too, don't you? > > > > In particular you can explain, how the empty set will emerge while > > > > throughout the whole time the minimum contents of the vase is 1 ball? > > > > Since outside of Wolkenmuekenheim there is no reason to > > > expect the number of balls to be continuous at infinity > > > Why then do you expect the digits of Cantor's diagonal number to be > > "continuous" at infinity (contrary to being *not* at infinity)? > > Why would anyone ever expect a numerical digit to be continuous? > > All the ones I am aware of are members of a finite set of discrete > objects.
And there is none that does not belong to a rational number. > > And why would you expect to find a digit of any sort "at infinity", when > there is no such a position as "at infinity".
If there is no "at infinity", then there cannot be a "behind infinity", so there is no omega and no omega + 1.
In fact you are right - as so often. There is no "at infinity". The vase is never empty. There is no smallest positive rational, There are not all rationals.