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 : 23. Nov 2024, 23:10:50
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <a7ec6cd4-3a9b-4671-8594-56586c0ce917@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 11/23/2024 4:39 PM, WM wrote:
On 23.11.2024 22:20, Jim Burns wrote:
Do you (WM) object to
k ↦ k+1 : one.to.one
>
I don't know what that waffle should mean.
k ↦ k+1 means the successor operation.
'One.to.one' means that,
if j≠k then j+1≠k+1
different numbers have different successors.
I am claiming that
different numbers have different successors.
Do you (WM) object to that claim?
E(k) ⊇ E(k+1)
|E(k)| ≥ |E(k+1)|
doesn't contradict
|E(k)| ≤ |E(k+1)|
>
It does.
Then you (WM) also don't know
what a contradiction is.
Together,
|E(k)| = |E(k+1)|
and
|E(k+1)| doesn't lose one number.
>
Spare your nonsense.
Nonsense such as
|E(k)| ≥ |E(k+1)| not.contradicting
|E(k)| ≤ |E(k+1)|
…