Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Thu, 16 Jan 2025 07:27:51 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <98d1b1111ef926cafe4bb1bea20016085f86e524@i2pn2.org>
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>
 <1ebbc233d6bab7878b69cae3eda48c7bbfd07f88@i2pn2.org>
 <vlo5f4$39hil$2@dont-email.me>
 <4c89380adaad983f24d5d6a75842aaabbd1adced@i2pn2.org>
 <vloule$3eqsr$1@dont-email.me>
 <ffffed23878945243684de7f2aa9aaaf29564508@i2pn2.org>
 <vlrej9$2m5k$1@dont-email.me> <d6ed4797-65e8-4004-853c-f07a37af0c11@att.net>
 <vls4j6$7v2k$3@dont-email.me> <494bfd3b-3c70-4d8d-9c70-ce917c15fc22@att.net>
 <vm0okb$16cq0$2@dont-email.me> <bff18686-503a-4b7b-9406-b47796f68b47@att.net>
 <vm15pj$18v7t$1@dont-email.me> <72142d82-0d71-460a-a1be-cadadf78c048@att.net>
 <vm3hrs$1s9ld$2@dont-email.me> <812e64b1-c85c-48ac-a58c-e8955bc02f8c@att.net>
 <vm59g4$2b5ib$1@dont-email.me> <b5040865-50e6-4297-a08c-0072e0a2cb0f@att.net>
 <vm8trc$30hqq$9@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Thu, 16 Jan 2025 12:27:51 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="3867329"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
X-Spam-Checker-Version: SpamAssassin 4.0.0
In-Reply-To: <vm8trc$30hqq$9@dont-email.me>
Content-Language: en-US

On 1/15/25 1:13 PM, WM wrote:
> On 14.01.2025 19:41, Jim Burns wrote:
>> On 1/14/2025 4:07 AM, WM wrote:
>>> On 13.01.2025 20:31, Jim Burns wrote:
>>>> On 1/13/2025 12:17 PM, WM wrote:
>>
>>>>> [...]
>>>>
>>>> A step is never from finite to infinite.
> 
> The dark realm is appears infinite.
>>>> There is no infinite set smaller than ℕ
>>>> #𝔼 ≥ #ℕ
>>>
>>> That is obviously wrong.
> 
>  The rule of subset proves that every proper subset has fewer elements 
> than its superset. So there are more natural numbers than prime numbers, 
> || > ||, and more complex numbers than real numbers, || > ||. Even 
> finitely many exceptions from the subset-relation are admitted for 
> infinite subsets. Therefore there are more odd numbers than prime 
> numbers || > ||.

Which doesn't apply to infinite sets.

Where are you getting your broken rules from.

> 
>  The rule of construction yields the number of integers || = 2|| + 1 
> and the number of fractions || = 2||2 + 1 (there are fewer rational 
> numbers # ). Since all products of rational numbers with an irrational 
> number are irrational, there are many more irrational numbers than 
> rational numbers || > |#|.

Yes, there are more irrational numbers thn rational numbers,

> 
>  The rule of symmetry yields precisely the same number of real 
> geometric points  in every interval (n, n+1] and with at most a small 
> error same number of odd numbers and of even numbers in every finite 
> interval and in the whole real line.
> 
>> There is no infinite set smaller than ℕ.
> 
> {2,3, 4, ...} is smaller by one element.

Which, since that size is infinite, is the same size.

A fact you don't seem to be able to understand, since your mind is stuck 
in finite arithmatic,

> 
> Regards, WM
> 
> 
>