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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Tue, 31 Dec 2024 19:20:14 +0100
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On 31.12.2024 18:25, Jim Burns wrote:
> On 12/29/2024 5:27 PM, WM wrote:

>> Every FISON is less than 1 % of ℕ
>> because
>> by expanding it by a factor 100
>> the situations remains the same - forever.
> </WM>
> Date: Tue, 31 Dec 2024 10:39:12 +0100
> Message-ID: <vl0e3v$25vs8$1@dont-email.me>
> 
> For each ordinal k, there is
> an ordinal k+1 which is fuller.by.one.
> ⎛ k = ⟦0,k⦆
> ⎝ k+1 = ⟦0,k⦆∪⦃k⦄

> For each room k, there is
> swap k⇄k+1

That does not disprove the theorem: Every union of FISONs which stay 
below a certain threshold stays below that threshold.
Note: Every FISON stays below 1 % of ℕ.
> Before any swap,
> Bob is in room 0
> 
> After swaps 0⇄1 1⇄2 ... k-1⇄k and
> before swap k⇄k+1
> Bob is in room k
> 
> ⎛ If Bob is in room k
> ⎜ them k⇄k+1 is not swapped
> ⎜
> ⎜ If Bob is in any room
> ⎜ then not all swaps are swapped

Bob is placed within the dark parts of the matrix.
> ⎜
> ⎜ For any claims P and Q
> ⎜ P⇒¬Q and Q⇒¬P are equally.true and equally.false
> ⎜
> ⎜ If all swaps are swapped
> ⎝ them Bob is not in any room.
Bob comes to rest within the dark part.
> 
>> Exchange of two entities does never result in
>> only one of them.
> 
> Two is finite.
> 
> How.many there are of
> all swaps, all rooms, or all finite.ordinals
> is more than any finite.ordinal,
> is more.than.finite.

Every exchange happens between two sites.
> 
> After all swaps,
> ⎛ Bob has never swapped into any darkᵂᴹ room,
> ⎝ Bob has swapped out of any visibleᵂᴹ room,

But Bob is never out of the matrix because there is no exchange at all 
between outside and inside.

Regards, WM