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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, 7 Jan 2025 11:20:40 +0100
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On 07.01.2025 02:36, Ross Finlayson wrote:
> On 01/06/2025 02:43 PM, Jim Burns wrote:

>> It would be great if you (WM) did NOT
>> find lemma 1 weird,
>> but it is what it is.

It is not weird. But your conclusions are weird.

> The inductive set being covered by
> initial segments is an _axiom_ of ZF.

And the existence of the set ℕ is also an axiom of ZF. Therefore ZF is 
incompatible with mathematics.

|ℕ| is a fixed quantity larger than every n, by any factor, for instance 
by the factor 100.

All FISONs stay below the threshold |ℕ|/100, or in other words, 
multiplication of any FISON by 100 is insufficient to cover |ℕ|.

Every union of FISONs {1, 2, 3, ..., n} which stay below this threshold 
stays below this threshold too.

Regards, WM