Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logicDate : 23. Nov 2024, 22:39:11
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vhti1v$1r2tr$2@dont-email.me>
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 23.11.2024 22:20, Jim Burns wrote:
On 11/23/2024 12:23 PM, WM wrote:
|E(k)| ≥ |E(k+1)| = |E(k)| - 1.
E(k) ⊇ E(k+1)
|E(k)| ≥ |E(k+1)|
doesn't contradict
|E(k)| ≤ |E(k+1)|
It does.
Together,
|E(k)| = |E(k+1)|
and
|E(k+1)| doesn't lose one number.
Spare your nonsense.
|E(k)| = |E(k+1)| is infinite.
The cardinality is an unsharp measure.
----
Do you (WM) object to
k ↦ k+1 : one.to.one
I don't know what that waffle should mean.
Regards, WM
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