Sujet : Re: Replacement of Cardinality
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.logicDate : 02. Aug 2024, 19:19:23
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <20de92387adf8636fd5677736135abedbbba5179@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
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.