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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: Mon, 20 Jan 2025 13:26:31 +0100
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On 19.01.2025 13:32, Richard Damon wrote:
> On 1/19/25 5:43 AM, WM wrote:

> 
> So, you admit that your FISONs are worthless?

No. FISONs are useful for showing the difference between the potentially 
infinite collection of definable numbers and the set ℕ.
> 
>> Name any FISON that is required to produce ℕ by a union of FISONs.
> 
> There is non, because you need almost ALL of the FISONS to do that,

Gobbledegook.
> 
>>
>> The set of required FISONs is well defined because for every FISON we 
>> can decide whether it is required in the union.
> 
> But YOU can only do that for a finite number of them, not almost all of 
> them.

Wrong. Every set of ordinal numbers has a first one.
> 
>>
>> Further, according to set theory, every well defined set of ordinal 
>> numbers has a first element. The FISONs F(n) must obey this theorem 
>> because they can be ordered by their greates ordinals n.
>>
>> You simply violate this fact.
> 
> Where? 

By not giving a first one.

>> The error is your handwaving claim that infinitely many FISONs are 
>> required. Infinitely many failures will not yield a success.
>>
> 
> And YOUR "handwaving" just shows your stupidity, and inability to 
> understand your stupidity.
> 
> I don't "Handwave" the claim of needing infinitely many FISONs,

I can prove that no FISON is required. That is mathematics.

Regards, WM