Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.logicDate : 24. Nov 2024, 21:17:21
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <68dc9b71-cf5d-4614-94e2-8a616e722a63@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
User-Agent : Mozilla Thunderbird
On 11/24/2024 2:42 PM, WM wrote:
On 24.11.2024 20:26, Jim Burns wrote:
What we mean by
|E(k)| ≤ |E(k+1)|
is that
there is a one.to.one function
from E(k) to E(k+1)
The successor operation, for example.
>
What I mean is the fact that
∀k ∈ ℕ: |E(k+1)| = |E(k)| - 1
whereas Cantor's ℵo is a very unsharp measure.
Finite cardinalities can change by 1.
Infinite cardinalities are larger than
each finite cardinality,
and cannot change by 1.
ℕ is the set of each and only finite cardinalities.
|ℕ| isn't a finite cardinality.
|ℕ| cannot change by 1.
So, there is.
So, |E(k)| ≤ |E(k+1)| isn't wrong.
>
Cantor's nonsense has many faces.
It i not suitable for serious maths.
Cardinalities which cannot change by 1
do not change by 1 when they're called unserious.
…