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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Replacement of Cardinality
Date: Fri, 2 Aug 2024 13:19:23 -0400
Organization: i2pn2 (i2pn.org)
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On 8/2/24 12:38 PM, WM wrote:
> Le 02/08/2024 à 18:19, Richard Damon a écrit :
> 
>> No, YOU THINK there are more algebraic numbers than prime numbers 
>> because you don't understand that there are exactly ℵo of both of them.
> 
> I know that ℵo is nonsense, because all prime numbers are algebraic but 
> not all algebraic numbers are prime. This does not change in the infinite.

Nope, infinite sets do not obey the same set of rules that finite sets 
do. Failure to understand that is YOUR problem, not the problem of those 
sets.

>>
>> All countably infinite sets are the same size,
> 
> That proves that ℵo is nonsense.
> 
> Regareds, WM
> 
> 

No, it proves that your logic can't handle it.

The fact you don't understand something doesn't make it wrong.

It just shows that your understanding is limited.

If you can show a contradiction in the system, USING THE RULES OF THE 
SYSTEM, then you might have something, but you can't try to impose rules 
you think "must be true" on the system.

Under your rules of "bounded logic" you can perhaps look into "potential 
infinity" but not fully understand it, but that logic totally breaks if 
you try to look at "actual infinity" as it creates concepts just totally 
foreign to it.