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| From | wm <wolfgang.mueckenheim@tha.de> |
|---|---|
| Newsgroups | sci.math |
| Subject | Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) |
| Date | 2026-03-26 17:33 +0100 |
| Organization | tha |
| Message-ID | <10q3n44$mnd9$1@solani.org> (permalink) |
| References | (12 earlier) <10pv0kr$1cmht$3@dont-email.me> <10q15b8$hh2u$1@solani.org> <10q17ja$1o6f$1@news.muc.de> <10q1ftr$28ttr$1@dont-email.me> <10q1jcm$1qbd$3@news.muc.de> |
Am 25.03.2026 um 22:17 schrieb Alan Mackenzie:
> WM <wolfgang.mueckenheim@tha.de> wrote:
>> Am 25.03.2026 um 18:55 schrieb Alan Mackenzie:
>
>>>> Look at the short Binary Tree of only two levels L1 and L2:
>
>>>> N0
>>>> / \
>>>> L1 N1 N2
>>>> / \ / \
>>>> L2 N3 N4 N5 N6
>>>> ...
>
>>>> The paths of the set P = {P(n) | n ∈ ℕ}, where node N(n) is mapped to
>>>> path P(n) ....
>
>>> ...., which you haven't defined, ....
>
>> That is not necessary for my proof.
>
>>>> .... fill the tree such that no further path can be distinguished.
>
>>> If you define path P(n) as the finite path between N0 and Nn, that
>>> subset of paths will indeed cover the tree.
>
>> My paths are infinite. P(n) runs from the root node to node Nn and then
>> continues infinitely.
>
> You have failed to define your paths. Just what nodes does path P(n)
> pass through below Nn?
You are free to choose the continuation under the condition that every
node belongs to at least one of my countable set of paths.
Note that in dsm the path turning always right has been proposed as
"diagonal path" (while all other paths turn left). This approach fails
because the right-side-path RRR... must belong to my set. As long as
nodes follow, they must be reached, but they can only be reached by the
utmost right poath RRR... .
>> If there is a path Q which is not considered, then it must deviate from
>> all considered paths P(n).
>
> Yes.
>
>> For that sake there must be a first node where it deviates from all.
>
> No. It must devate from each other path at a node specific to that path.
Wrong. In order to prove that the set is uncountable, you must construct
at least one path that deviates from the countable set.
>
>> But there is none. Note: When it deviates only from some given P(n)
>> but continues in another path, then it is this other path.
>
> Again, you haven't defined your paths. But a strategy for finding a path
> different from all in your countable set is as follows:
>
> (i) Start from node N0.
> (ii) At each node we pass through:
> (a) identify the first path P(m) in the countable collection which
> passes through the current node.
> (b) Extend the new path by going to node in the next level different
> from where P(m) went.
That follows a path containing this different node. Every node is
covered by the countable set.
> (v) Repeat steps (ii)(a) and (ii)(b) indefinitely.
Fail indefinitely.
>
> It will be seen that the new path is different from each path P(n) in the
> countable collection. Thus the supposedly complete collection of
> infinite paths is incomplete. I.e. the number of paths is uncountable.
That can only be proven by a path not belonging to the countable set.
This path must leave all others at some node. But every node is occupied
already. No chance.
Regards, WM
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Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-03-24 21:44 +0000
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-24 19:31 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-24 19:32 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-24 20:07 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-25 14:04 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-04-04 20:54 +0100
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) wm <wolfgang.mueckenheim@tha.de> - 2026-03-25 18:17 +0100
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Alan Mackenzie <acm@muc.de> - 2026-03-25 17:55 +0000
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) WM <wolfgang.mueckenheim@tha.de> - 2026-03-25 21:18 +0100
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Alan Mackenzie <acm@muc.de> - 2026-03-25 21:17 +0000
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) WM <wolfgang.mueckenheim@tha.de> - 2026-03-25 22:53 +0100
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-25 15:08 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-26 10:28 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) wm <wolfgang.mueckenheim@tha.de> - 2026-03-26 17:33 +0100
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Alan Mackenzie <acm@muc.de> - 2026-03-26 17:34 +0000
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) WM <wolfgang.mueckenheim@tha.de> - 2026-03-26 21:08 +0100
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-27 09:21 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-03-26 12:22 +0000
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Alan Mackenzie <acm@muc.de> - 2026-03-26 12:40 +0000
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-03-26 13:09 +0000
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Alan Mackenzie <acm@muc.de> - 2026-03-26 13:40 +0000
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Moebius <invalid@example.invalid> - 2026-04-30 04:43 +0200
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-30 09:10 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Mikko <mikko.levanto@iki.fi> - 2026-05-01 11:55 +0300
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 09:47 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) wm <wolfgang.mueckenheim@tha.de> - 2026-05-01 15:20 +0200
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