On 20 Jun., 15:33, "Julio Di Egidio" <ju...@diegidio.name> wrote: > "WM" <mueck...@rz.fh-augsburg.de> wrote in message > > news:firstname.lastname@example.org... > > > On 20 Jun., 03:31, "Julio Di Egidio" <ju...@diegidio.name> wrote: > >> "fom" <fomJ...@nyms.net> wrote in message > > >>news:C6KdnZCccIjltVzMnZ2dnUVZ_t6dnZ2d@giganews.com... > > >> > "Numbers count themselves" > > >> Indeed, how else? > > > In matheology there are n numbers (1, 2, ..., n) but omega or aleph_0 > > numbers (1, 2, 3, ...) and omega + 1 numbers > > (1, 2, 3, ..., omega). This observation initially caused me to refuse set theory. > > That kind of observation is exactly where I am coming from, should you have > not noticed.
So we have something in common.
> But I am sick of your as well as my own hand-waving: Have you > got any reference that could help me make head or tails of the [0, lamba) vs > [0, lambda] issue?
The observation that omega or aleph_0 or |N is a number that counts all natural numbers but is larger than all natural numbers, is not usually recognized in set theoty. And if it is recognized, it is covered with silence. Therefore all matheologians try to find some "explanation" why
1 2, 1 3, 2, 1 ...
has no line |N but all columns are |N.
And if you write all lines into one and the same line, you get |N = ... 3, 2, 1. And if you union all lines, you get |N too, although each line lacks infinitely many natural numbers and the set of lines is inclusion monotonic.
I think these observations should show to every sober mind that finished infinity is as self-contradictory as the name says.
> (E.g. did anybody study the latter construction? Does > the "issue" exists at all,
This issue does not exist in any forum or journal where matheologians are the dominating fraction. In MathOverflow for instance such questions are quickly deleted in order to prevent that newbies may get to know that argument befor their brains have been completely perverted by the "formalism" of matheology. After two or three years they are unable to understand or at least unwilling to accept that their complete work has been in vain as completed nonsense.