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Re: Difficult question

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Gus Gassmann schrieb am Donnerstag, 11. Mai 2023 um 00:20:49 UTC+2:
> On Wednesday, 10 May 2023 at 10:02:51 UTC-3, WM wrote: 
> > Fritz Feldhase schrieb am Dienstag, 9. Mai 2023 um 19:50:00 UTC+2: 
> > > On Tuesday, May 9, 2023 at 7:08:12 PM UTC+2, WM wrote: 
> > > 
> > > > All [...] endsegments E(n) of natural numbers 
> > > > E(n) = {n, n+1, n+2, ...} 
> > > > contain ℵo natural numbers. [...] 
> > > > 
> > > > A [certain] bijection with the initial segments 
> > > > I(n) = {1, 2, 3, ..., n} 
> > > > produces the pairs 
> > > > 
> > > > ({1}, {1, 2, 3, ...,}) 
> > > > ({1, 2}, {2, 3, 4, ...,}) 
> > > > ({1, 2, 3}, {3, 4, 5, ...,}) 
> > > > ... 
> > > > ({1, 2, 3, ..., n}, {n, n+1, n+2, ...}) 
> > > > ... 
> > > Right. Actually, it's the bijection f: {I(n) : n e IN} --> {E(n) : n e IN} defined with f(x) = E(max(x)) for all x in {I(n) : n e IN}. 
> > > Actually, f = {({1}, {1, 2, 3, ...,}), ({1, 2}, {2, 3, 4, ...,}), ({1, 2, 3}, {3, 4, 5, ...,}), ..., ({1, 2, 3, ..., n}, {n, n+1, n+2, ...}), ...} 
> > > 
> > > and [by definition of f]: ({1, 2, 3, ...}, { }) !e f. 
> > Every endsegment is a term of the sequence. At every step one natnumber is lost. As long as only finitely many natnumbers have been lost and the terms are infinite, the sequence has only finitely many terms and is a finite sequence.
> Quite so. And once you have collected infinitely many different such sets

There are not enough to collect.

> to remove (no matter which ones they are), their intersection is empty.

Up to every infinite endsegment, i.e., an endsegment that misses only finitely many natnumbers, the sequence of losses is finite.

Regards, WM

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Difficult question WM <askasker48@gmail.com> - 2023-05-09 10:08 -0700
  Re: Difficult question Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-09 10:49 -0700
    Re: Difficult question WM <askasker48@gmail.com> - 2023-05-10 06:02 -0700
      Re: Difficult question Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-10 15:20 -0700
        Re: Difficult question WM <askasker48@gmail.com> - 2023-05-11 04:40 -0700
          Re: Difficult question Jim Burns <james.g.burns@att.net> - 2023-05-11 16:11 -0400
            Re: Difficult question Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-11 13:30 -0700
            Re: Difficult question WM <askasker48@gmail.com> - 2023-05-12 05:37 -0700
              Re: Difficult question Jim Burns <james.g.burns@att.net> - 2023-05-12 14:18 -0400
                Re: Difficult question WM <askasker48@gmail.com> - 2023-05-13 06:14 -0700
                Re: Difficult question Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-05-14 08:46 -0700
                Re: Difficult question WM <askasker48@gmail.com> - 2023-05-14 13:47 -0700
          Re: Difficult question Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-11 14:01 -0700
            Re: Difficult question Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-11 14:28 -0700
              Re: Difficult question Gus Gassmann <horand.gassmann@gmail.com> - 2023-05-12 01:34 -0700
                Re: Difficult question Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-12 08:53 -0700
                Re: Difficult question Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-14 08:41 -0700
                Re: Difficult question Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-14 10:33 -0700
                Re: Difficult question Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-14 10:38 -0700
                Re: Difficult question Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-14 11:48 -0700
            Re: Difficult question WM <askasker48@gmail.com> - 2023-05-12 05:38 -0700

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