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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 17 Nov 2024 19:08:54 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sun, 17 Nov 2024 18:38:00 +0100 schrieb WM:
> On 17.11.2024 17:59, FromTheRafters wrote:
>> WM pretended :
>>> On 17.11.2024 12:38, FromTheRafters wrote:
>>>> WM presented the following explanation :
>>>>> On 17.11.2024 12:01, FromTheRafters wrote:
>>>>>> WM was thinking very hard :
>>>>>>> On 16.11.2024 22:33, Moebius wrote:
>>>>>>>
>>>>>>>> For example "aleph_0 - aleph_0" is not defined.
>>>>>>>
>>>>>>> Small wonder. ℵo means only infinitely many: |ℕ|, |ℚ|, and many
>>>>>>> others. |ℕ|-|ℕ| however is defined.
>>>>>>
>>>>>> No, it is not.
>>>>>
>>>>> If sets are invariable then ℕ \ ℕ is empty.
>>>>> If |ℕ| concerns only the elements of ℕ, then |ℕ|-|ℕ|= 0.
>>>>
>>>> So, you're saying that if I take aleph_zero natural numbers and I
>>>> remove the aleph_zero odd numbers from consideration in a new set, I
>>>> will have a new emptyset instead of E?
>>>
>>> Try to understand. "aleph_0 - aleph_0" is not defined.
>> Try to understand that |N| equals aleph_zero.
> 
> Of course. ℵo equals |ℕ|, equals |ℚ|, equals all countable sets. It is
> simply another name for infinitely "many". |ℕ| however is a fixed
> infinite number. Note that sets are invariable.

Yes, those are all the same number.

-- 
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.