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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: Fri, 10 Jan 2025 18:28:04 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Fri, 10 Jan 2025 18:21:43 +0100 schrieb WM:
> On 10.01.2025 18:01, joes wrote:
>> Am Fri, 10 Jan 2025 17:19:44 +0100 schrieb WM:
>>> On 10.01.2025 13:41, Richard Damon wrote:
>>>> On 1/9/25 7:37 AM, WM wrote:
>>
>>> Infinite is simply infinite, no matter what the real size is.
>> There is no "real size", there is only the set.
> There is real size. The natural numbers have twice the size of the even
> numbers.
No, the even numbers are twice the naturals.

>> Your expectations about cardinality do not match it.
> I have no expectations about cardinality. I know that for every finite
> initial segment the even numbers are about half of the natural numbers.
> This does not change anywhere. It is true up to every natural number.
> More are not available.
You wrongly expect this to hold in the infinite.

>>> You need not understand that. But the claim that different sets like ℕ
>>> and ℚ are of same size shows that you have been stultified by set
>>> theory.
>> They have the same cardinality, defined as being bijective.
> Already the bijection between even and natural numbers has been
> disproved above.
You are mistaken. Clearly |{1*2, 2*2, 3*2, ...}| = |N|

-- 
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.