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

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 255
Posted: Apr 20, 2013 5:36 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 20 Apr., 22:32, Virgil <vir...@ligriv.com> wrote:
>

> > > mathematics how all n can be in the union of all s_i without all n
> > > being in one and the same s_i.

> >
> > Simple! At least everywhere outside of Wolkenmuekenheim:
> >
> >    For all i in |N, s_(i+1) \ s_i = i+1,
> > and
> >    For all i in |N, i is a member of s_1.

>
> No.

> >
> > 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.

> 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 in WM's world.

But OUTSIDE WM's world, NOT all naturals can be in an one FISON, s_n
>
> If only ~(n e s_j) & n e s_k, then also m e s_k is possible, and then
> n and m are in s_k. No evidence that not all naturals in one s.

Maybe no such evidence in Wolkenmuekenheim, but there is enough outside
Wolkenmuekenheim, to satisfy everyone other than WM.

For every i in |N, max(s_i) = i and i+1 is not in s_i.

Which is sufficient evidence OUTSIDE WOLKENMUEKENHEIM to show that not
all naturals are in any one of the s_i,
at least not OUTSIDE WOLKENMUEKENHEIM .
--

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
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 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/20/13 fom
4/20/13 fom
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