Path: eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Tue, 26 Nov 2024 06:15:08 -0500
Organization: Peripheral Visions
Lines: 22
Message-ID: <vi4ak0$3e1nc$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vhprpj$15kfd$2@dont-email.me> <74bdc0f14fd0f2c6bfd9ac511a37f66b41948ac4@i2pn2.org> <vhq5ov$1793m$2@dont-email.me> <b82423aaf8df2203171c1eb1afcb913925875795@i2pn2.org> <vhqrsu$1bb1f$2@dont-email.me> <vhqu9n$1bqev$1@dont-email.me> <vhs9v9$1krl6$3@dont-email.me> <vhshas$1n123$1@dont-email.me> <vhsi31$1n2ck$1@dont-email.me> <vhsi7e$1n4sl$1@dont-email.me> <vhsit2$1n52r$1@dont-email.me> <vht7o6$1qo7j$1@dont-email.me> <vhtb3o$1r2tr$1@dont-email.me> <0d6d06a888e15ed2042aca8ec7e6ebb93590b7bc@i2pn2.org> <vhtgec$1rdku$3@dont-email.me> <8a2aedd8383a84ceef2fd985ac0bf529e2a0eccf@i2pn2.org> <vhuv94$25ro0$1@dont-email.me> <be7b74a5d83b8ceebd1ec380bb57ff4190ec0cae@i2pn2.org> <vhv61v$25uqa$5@dont-email.me> <b75deca6b1a0631255cf1402ee83db2b266edd22@i2pn2.org> <vhvnvc$2aq7k$1@dont-email.me> <3fe6ef31f562e0ddf598de46cf864986ca909687@i2pn2.org> <vi1pul$2n5v3$1@dont-email.me> <9cb8aec671200bb6d71582fd607b876b7ec4c83a@i2pn2.org> <vi43br$3cllo$3@dont-email.me>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 26 Nov 2024 12:15:13 +0100 (CET)
Injection-Info: dont-email.me; posting-host="e38c8520a2c3bc82cd2c5bf8f6d7cb18";
	logging-data="3606252"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19gfPrxgOaf4a8Eccm+XIbVbAZZc6YG3ok="
Cancel-Lock: sha1:H6LhWdpmVhbQ+UyZiTJQuSRW2lA=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376

WM pretended :
> On 25.11.2024 22:05, joes wrote:
>> Am Mon, 25 Nov 2024 13:18:28 +0100 schrieb WM:
>
>>>> But there is no finite set with ALL natural numbers.
>>>> Like usual, you mess up with your qualifiers.
>>> ℕ is fixed, that means |ℕ| is fixed.
>> What does that have to do with it?
>
> It is impossible to add or to delete an element.

However, one can make a new set by considering another element not 
previously considered in a set, or by not considering one of the 
previously considered elements. Sets don't change, but new sets can be 
made.

> It is impossible to change |ℕ| by 1 or more.

Right, sets don't change. The set {2,3,4,...} does not equal the set of 
natural numbers, but |{2,3,4,...}| does equal |N|.

[...]