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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: Fri, 13 Dec 2024 12:25:38 +0100
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On 13.12.2024 06:06, Jim Burns wrote:
> On 12/12/2024 5:11 PM, WM wrote:
>> On 12.12.2024 17:15, Jim Burns wrote:
> 
>>> The existence of a bridge implies that,
>>> somewhere we can't see,
>>> a size which cannot change by 1
>>> changes by 1 to
>>> a size which can change by 1
>>
>> Every set can change by one element.
>> No size is required and no size is possible
>> if this is forbidden.
> 
> Ignoring cardinality changes nothing
> about f(k) = k∪{k} and ⟦0,w⦆ and ⟦1,w⦆

Ignoring that Cantor's claim requires to empty the endsegments from all 
natural numbers in order to use them as indices in mappings (ℕ to the 
set of endsegments, ℕ to ℚ, ℕ to the lines of the Cantor list for 
"proving" the uncountability of ℝ) shows inconsistency.

Remark: The mapping from ℕ to the set of endsegments is one of the few 
true bijections.

Regards, WM