Sujet : Re: how
De : chris.m.thomasson.1 (at) *nospam* gmail.com (Chris M. Thomasson)
Groupes : sci.mathDate : 17. Apr 2024, 19:54:26
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <uvp5t2$1oghe$3@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 4/17/2024 11:49 AM, WM wrote:
Le 17/04/2024 à 01:27, Richard Damon a écrit :
On 4/16/24 10:59 AM, WM wrote:
Note, no "Natural Number" is actually infinite, that distinction falls on omega. But the SET of the Natural Numbers is Actually Infinite in Size, having a size of Aleph_0.
The size of ℕ is |ω|. That means ℕ extends on the ordinal line from 0 to ω. By multiplying every natural number the extendion is doubled. That is mathematics. Every contrary opinion is foolish.
>
Does that mean the Natural Numbers themselves are individually only "Potentially Infinite" but the set of them is "Actually Infinite" by your definitions?
The visible natural numbers are potentially infinite. The set ℕ is assumed to be actualy infinite. This cannot be known let alone be proven.
The set of natural numbers is infinite... What is wrong with you, damn it!
;^o
But we can assume it and draw conclusions. One of them is that nothing fits between all natural numbers and ω.
Rolling eyes....
Re: Contradiction of bijections as a measure for infinite sets
Re: how