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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 15 Dec 2024 12:39:05 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sun, 15 Dec 2024 12:33:15 +0100 schrieb WM:
> On 15.12.2024 12:03, Mikko wrote:
>> On 2024-12-14 09:50:52 +0000, WM said:
>>> On 14.12.2024 09:52, Mikko wrote:
>>>> On 2024-12-12 22:06:58 +0000, WM said:

>>>> is Dedekind-infinte:
>>>> the successor function is a bijection between the set of all natural
>>>> numbers and non-zero natural numbers.
>>> This "bijection" appears possible but it is not.
>> So you say that there is a natural number that does not have a next
>> natural number. What number is that?
> We cannot name dark numbers as individuals.
Shame.
> All numbers which can be
> used a individuals belong to a potentially infinite collection ℕ_def.
> There is no firm end. When n belongs to ℕ_def, then also n+1 and 2n and
> n^n^n belong to ℕ_def.
And thus all n e N do.

> The only common property is that all the numbers
> belong to a finite set and have an infinite set of dark successors.
If all successors belong to N_def, it can’t be finite and the
successors can’t be dark.

> This is the only way to explain that the intersection of endegments
> E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ...
> loses all content in a sequences which allow the loss of only one number
> per step.
The explanation is that the sequence is infinitely long.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.