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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: Sat, 11 Jan 2025 10:25:58 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 11 Jan 2025 11:04:56 +0100 schrieb WM:
> On 11.01.2025 01:28, Richard Damon wrote:
>> On 1/10/25 4:48 PM, WM wrote:
>>> On 10.01.2025 21:08, Jim Burns wrote:
>>>
>>>> Where OUR infinityⁿᵒᵗᐧᵂᴹ "doesn't work",
>>>> it's you who's saying it doesn't work,
>>> You are inconsistent. You claim that all natural numbers are an
>>> invariable set. But when all elements are doubled then your set grows,
>>> showing it is not invariable. That is nonsense.
>> But the set doesn't grow.
>> Which element is in the doubled set that wasn't there in the first
>> place?
> The number of elements remains constant. All odd numbers of ℕ are
> deleted. That implies that new even numbers are added.
Nope. This is all just your conception of Aleph_0 as finite. It does
not behave like that. All countable sets are bijective to each other.

> "The infinite sequence thus defined has the peculiar property to contain
> the positive rational numbers completely, and each of them only once at
> a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]
This just means it is a bijection to N, which has an order.

> If Cantor has constructed a sequence containing all even numbers of the
> original set ℕ, then the doubled even numbers are missing.
What? Doubled even numbers are also even numbers.

-- 
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.