Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 12 Jan 2025 16:25:15 +0100
Organization: A noiseless patient Spider
Lines: 23
Message-ID: <vm0mss$16cq1$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>
 <66868399-5c4b-4816-9a0c-369aaa824553@att.net> <vlir7p$24c51$1@dont-email.me>
 <417ff6da-86ee-4b3a-b07a-9c6a8eb31368@att.net> <vllfof$2n0uj$2@dont-email.me>
 <07258ab9-eee1-4aae-902a-ba39247d5942@att.net> <vlmst2$2vjr0$3@dont-email.me>
 <ff1fe002014bf5951a98e2061cb63ad93976a808@i2pn2.org>
 <vlofv2$3akpn$1@dont-email.me>
 <9f6faf842a0202b345f3912fe352044dfabfc56d@i2pn2.org>
 <vlrhb0$2m5j$1@dont-email.me>
 <5e1c366f8e2cfe7f5439f3d2bb65d4695d17c6b9@i2pn2.org>
 <vlrkv7$5ent$1@dont-email.me>
 <e47acb80f38537e615ac913cfec68cf6d7d498ae@i2pn2.org>
 <vlrroh$6ovc$2@dont-email.me>
 <2c1e0afa5652b5f139abcda8822ac14ccc939f2b@i2pn2.org>
 <vls41b$7v2k$1@dont-email.me>
 <14c40a8944eb8e3ffc72ceed400106b988340891@i2pn2.org>
 <vltbbq$heoh$2@dont-email.me>
 <2734a9c30b5cddf6be417bb317be9b28e6236e66@i2pn2.org>
 <vltljs$heoh$9@dont-email.me>
 <c9b24ac0b53d76802b6d0a8c50a48861d2c9e529@i2pn2.org>
 <vm08fj$14gkv$1@dont-email.me>
 <454966b77264798056715a6751287437b31bd113@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 12 Jan 2025 16:25:16 +0100 (CET)
Injection-Info: dont-email.me; posting-host="12b77b53e2dfb1366c2321c2e7d191b6";
	logging-data="1258305"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19+4HoDNb4kr8QOtYs0uDv+TxtBM260dfw="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:HuOsmW3W2p8KX4Id8ezt/VxRhdw=
Content-Language: en-US
In-Reply-To: <454966b77264798056715a6751287437b31bd113@i2pn2.org>
Bytes: 2956

On 12.01.2025 14:29, joes wrote:
> Am Sun, 12 Jan 2025 12:19:15 +0100 schrieb WM:
>> On 11.01.2025 14:58, joes wrote:
>>> Am Sat, 11 Jan 2025 12:44:59 +0100 schrieb WM:
>>
>>>>>>>> ∀n ∈ ℕ: |{1, 2, 3, ..., 2n}|/|{2, 4, 6, ..., 2n}| = 2.
>>> Your claim does not hold for the sets.
>> That may be if sets are considered as more than their elements. My
>> claims hold for all their elements.
> I am talking about the sets N and E. They are infinite, so you are
> saying nothing about them, only about finite subsets.

Wrong. I am talking about all numbers which Cantor uses for his 
bijections. He uses only elements, not sets.

"The infinite sequence thus defined has the peculiar property to contain 
the positive rational numbers completely"

"thus we get the epitome (ω) of all real algebraic numbers."

For all these numbers my equations are true.

Regards, WM