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Topic: Matheology § 255
Replies: 69   Last Post: Apr 24, 2013 9:49 PM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 255
Posted: Apr 20, 2013 5:44 PM

On 20 Apr., 23:36, Virgil <vir...@ligriv.com> wrote:

> > > Thus for every s_i there is i+1 in |N not in s_i, but Union(S) = |N.
>
> > That is trivial and requires no explanation.
>
> > U s_i = |N.
>
> > But either there are all naturals in one s or not.
> > That is simple TND.

>
> And since for EVERY such s, max(s) + 1 is NOT a member of s, there
> cannot be all natruals in any s.

Then for all j: there is an n not in s_j.
Does the union contain more naturals than the complete sequence?

>
> > If *not* all naturals in one s, then
> > exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k.

>
> Once before claimed and also once beforE DEBUNKED.
>
> NOTE that a e s_b iff a <= b and ~( a e s_b) iff a > b, so that
>    m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k
> iff
>    (m <= j) & (m > k) & (n >j) & ( n <= k)
> But  if (m <= j)  & (n >j) then m < n
> And  if (m > k) & (n <= k) then  n < m
> So it follows that m > m and n > n, at least

if all naturals are in the terms s_i of S but not all are in one s_i.
Yes, that's the contradiction.

Otherwise there are more naturals in the union than in the terms of
the sequence. That would be another contradiction.

Regards, WM

Date Subject Author
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 David C. Ullrich
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Bergholt Stuttley Johnson
4/20/13 Virgil
4/20/13 fom
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/20/13 Virgil
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Virgil
4/20/13 Virgil
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Virgil
4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 Virgil
4/20/13 fom
4/20/13 Virgil
4/20/13 fom
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4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
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4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
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4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 Virgil
4/20/13 Virgil
4/20/13 Virgil
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 fom
4/21/13 Virgil
4/22/13 mueckenh@rz.fh-augsburg.de
4/22/13 Virgil
4/23/13 mueckenh@rz.fh-augsburg.de
4/23/13 Virgil
4/24/13 mueckenh@rz.fh-augsburg.de
4/24/13 Virgil
4/24/13 mueckenh@rz.fh-augsburg.de
4/24/13 Virgil
4/24/13 fom
4/23/13 gus gassmann
4/20/13 fom
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Virgil
4/20/13 Virgil