Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!border-1.nntp.ord.giganews.com!nntp.giganews.com!Xl.tags.giganews.com!local-4.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 12 Jan 2025 16:20:57 +0000
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Newsgroups: sci.math
References: <vg7cp8$9jka$1@dont-email.me> <vlc68u$k8so$1@dont-email.me>
 <vldpj7$vlah$7@dont-email.me>
 <a8b010b748782966268688a38b58fe1a9b4cc087@i2pn2.org>
 <vlei6e$14nve$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$3@dont-email.me>
 <adef9ec5c327614374fdc3c3cc55d7a753e28a36@i2pn2.org>
 <vltfo8$heoh$5@dont-email.me>
 <7fc40cc2dbd42016a62aa0374d545e9e787a7da3@i2pn2.org>
 <vltu35$lav6$1@dont-email.me> <vm0a73$14qpl$1@dont-email.me>
 <vm0ar4$14ugc$1@dont-email.me>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 12 Jan 2025 08:20:56 -0800
User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101
 Thunderbird/38.6.0
MIME-Version: 1.0
In-Reply-To: <vm0ar4$14ugc$1@dont-email.me>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Message-ID: <-NGdnauPY7t0dh76nZ2dnZfqn_idnZ2d@giganews.com>
Lines: 31
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-KzfcCcZjX/g0d3qlmP9qRR9loN1AAxqIMUEY/AAPz27I/9cNAM03F1GghYoQ67k9MQcTNbucfzVol8a!aYjqpKUJq/TDXtfxys842lLRgp5IRFUj7TYvWPULo9e54uqoO8v4uLpx8zG3+C4gnCHX4lHMtZQ=
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40

On 01/12/2025 03:59 AM, FromTheRafters wrote:
> WM submitted this idea :
>> On 11.01.2025 15:09, FromTheRafters wrote:
>>> joes laid this down on his screen :
>>>> Am Sat, 11 Jan 2025 11:04:56 +0100 schrieb WM:
>>
>>>>> 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.
>>>
>>> He's a hopeless case.
>>
>> Yes, you cannot hope ever to understand the difference between
>> potential and actual infinity.
>
> I've yet to see any useful application of the notion of potential
> infinity. IMO it was created to appease the philosophers and later
> rejected as useless by modern mathematicians.
>
>> In actual infinity all numbers are present. No one is missing,
>> according to Cantor. None can be added.
>> If you multiply every number by 2, then larger even numbers than all
>> hitherto present even numbers are created because the number of
>> numbers remains constant but the odd numbers disappear.
>
> Wrong, the numbers are not 'created' as they already existed.

Ah, a true mathematical platonism, ....