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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Tue, 19 Nov 2024 12:05:51 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Mon, 18 Nov 2024 23:16:22 +0100 schrieb WM:
> On 18.11.2024 22:58, FromTheRafters wrote:
>> on 11/18/2024, WM supposed :
>>> On 18.11.2024 18:15, FromTheRafters wrote:
>>>> WM brought next idea :
>>>
>>>>>> |ℕ| - |ℕ| = 0 because if you subtract one element from ℕ then you
>>>>>> have no longer ℕ and therefore no longer |ℕ| describing it.
|N\{0}| = |N| = Aleph_0

>>> If you remove one element from ℕ, then you have still ℵo but no longer
>>> all elements of ℕ.
>> But you do have now a proper subset of the naturals the same size as
>> before.
> It has one element less, hence the "size" ℵo is a very unsharp measure.
You can still say it is a subset, like Cantor did with "reality".

>>> If |ℕ| describes the number of elements, then it has changed to |ℕ| -
>>> 1.
>> Minus one is not defined.
> Subtracting an element is defined. |ℕ| - 1 is defined as the number of
> elements minus 1.
And |N\{2}| = Aleph_0.

>>> If you don't like |ℕ| then call this number the number of natural
>>> numbers.
>> Why would I do that when it is the *SIZE* of the smallest infinite set.
> The set of prime numbers is smaller.
There are infinitely many of them. 

-- 
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.