Path: ...!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 16 Dec 2024 18:57:59 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <4efa80aa8ba6633e37130c0374e2f44d4c89c8a3@i2pn2.org>
References: <vg7cp8$9jka$1@dont-email.me> <vi224l$2pgrd$1@dont-email.me>
 <vi4383$3csd4$2@dont-email.me> <vi4a6c$3dt4s$2@dont-email.me>
 <vi6p1l$3uoti$1@dont-email.me> <vi6unr$3v0dn$5@dont-email.me>
 <vihd3l$2d9fk$1@dont-email.me> <vihfai$2cnof$1@dont-email.me>
 <vijrru$37ce1$1@dont-email.me> <vikh9k$3cua3$1@dont-email.me>
 <viml28$6j3$1@dont-email.me> <0b1bb1a1-40e3-464f-9e3d-a5ac22dfdc6f@tha.de>
 <95183b4d9c2e32651963bac79965313ad2bfe7e8@i2pn2.org>
 <vj6vhh$elqh$2@dont-email.me>
 <33512b63716ac263c16b7d64cd1d77578c8aea9d@i2pn2.org>
 <vj9s4i$11a3p$1@dont-email.me> <vjam6d$1700v$1@dont-email.me>
 <vjc65g$1i9vk$3@dont-email.me> <vjf7kl$2s7e5$1@dont-email.me>
 <vjfmq3$2upa9$3@dont-email.me> <vjjh0o$3u5ec$1@dont-email.me>
 <vjjkds$3ukck$1@dont-email.me> <vjmd21$hq8s$1@dont-email.me>
 <vjmepr$hk44$2@dont-email.me>
 <aa42107d707ba33ffeca0d8788beb98043794604@i2pn2.org>
 <vjnbin$lspo$3@dont-email.me>
 <67e587a384538d7d311613630232bf025415e67b@i2pn2.org>
 <vjoq5d$11n0g$6@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 16 Dec 2024 23:57:59 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="3217136"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
Content-Language: en-US
In-Reply-To: <vjoq5d$11n0g$6@dont-email.me>
X-Spam-Checker-Version: SpamAssassin 4.0.0
Bytes: 2907
Lines: 27

On 12/16/24 3:59 AM, WM wrote:
> On 15.12.2024 22:14, Richard Damon wrote:
>> On 12/15/24 2:44 PM, WM wrote:
>>> On 15.12.2024 13:54, Richard Damon wrote:
>>>>
>>>> You can't "name" your dark numbers,
>>>
>>> because they are dark.
> 
>>> |ℕ \ {1, 2, 3, ...}| = 0 cannot be accomplished by visible numbers 
>>> because ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> 
>> Which just shows that the full set in infinte, and any member in it is 
>> finite, and not the last member.
> 
> Many members can be subtracted individually but infinitely many members 
> cannot be subtracted individually. They are belonging to the set. They 
> are dark.
> 
> Regards, WM
> 

Sure an infinite number of members can be subtracted individually, if 
you logic allows for infinite operations.

Since yours doesn't you run into the problem that you never got the set 
of the Natural Numbers in the first place, so you system just colapses 
on its own lies.