Path: ...!Xl.tags.giganews.com!local-3.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Mon, 30 Dec 2024 01:17:51 +0000
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Newsgroups: sci.math
References: <vg7cp8$9jka$1@dont-email.me> <vjjg6p$3tvsg$1@dont-email.me>
 <c31edc62508876748c8cf69f93ab80c0a7fd84ac@i2pn2.org>
 <vjka3b$1tms$3@dont-email.me>
 <e11a34c507a23732d83e3d0fcde7b609cdaf3ade@i2pn2.org>
 <vjmse3$k2go$2@dont-email.me>
 <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org>
 <vjooeq$11n0g$2@dont-email.me>
 <2d3620a6e2a8a57d9db7a33c9d476fe03cac455b@i2pn2.org>
 <vjrfcc$1m1b2$1@dont-email.me>
 <75921cc1f17cdb691969a99e666f237cd09c0b09@i2pn2.org>
 <vjsrp1$1tqvv$2@dont-email.me>
 <25729298b142c60d5b245231984119d42d4ac089@i2pn2.org>
 <vko14j$53b6$3@dont-email.me> <vko1vp$5mmo$1@dont-email.me>
 <vkp06p$b7kj$1@dont-email.me>
 <8a5ea464a97000a9e3e8cad62bd9d2a0f5aa5742@i2pn2.org>
 <vkradm$tpqs$2@dont-email.me>
 <cb53956e1b9f9f294eabe4bb2931aec79af363ad@i2pn2.org>
 <4z6dnRakN8kgDOz6nZ2dnZfqn_sAAAAA@giganews.com>
 <727cd9d4-df50-4a44-8529-cfc5dfb39bcb@att.net>
 <LdWcnZphF9MjKuz6nZ2dnZfqnPqdnZ2d@giganews.com>
 <ce9d3f75-33f5-414f-b3fa-00b5aa8a2e2d@att.net>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 29 Dec 2024 17:17:45 -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: <ce9d3f75-33f5-414f-b3fa-00b5aa8a2e2d@att.net>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Message-ID: <L0ednSxOItgiaez6nZ2dnZfqn_YAAAAA@giganews.com>
Lines: 39
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-9Bs9AyGkj8gzRuASPDq+yA8NhxetdIcswuEMtOINkXk7/50T5LkftSSOV8cXMeabKawjqPCCYXFYa5V!LShkPLpQfddUDkhBAcqo8oIv11wjd7tP3EF/C/6EBeCj+WFjYP8Uh4lHs4GsfEd1MxuUObUY1Ws=
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
Bytes: 3209

On 12/29/2024 01:48 PM, Jim Burns wrote:
> On 12/29/2024 3:57 PM, Ross Finlayson wrote:
>> On 12/29/2024 12:34 PM, Jim Burns wrote:
>>> On 12/29/2024 1:15 PM, Ross Finlayson wrote:
>>>> On 12/29/2024 06:43 AM, joes wrote:
>
>>>>> The infinite union doesn’t.
>>>>
>>>> There is no "infinite union" in ZF,
>>>> only "pair-wise union",
>>>> according to the axiom of union.
>>>
>>> No.
>>> https://en.wikipedia.org/wiki/Axiom_of_union
>>> ⎛ Informally, the axiom states that
>>> ⎜ for each set x there is a set y
>>> ⎜ whose elements are precisely
>>> ⎝ the elements of the elements of x.
>>
>> "In-formally [naively], ...."
>
> 'Informally' isn't 'naively'.
>
> ⎛ In the formal language of the Zermelo–Fraenkel axioms,
> ⎜ the axiom reads:
> ⎝ ∀A∃B∀c(c∈B⟺∃D(c∈D∧D∈A))
> -- ibid.
>
>

Yeah, "pair-wise".

I'm telling you, I am not wrong,
and for a long time, I am not under-informed,
about ZF and ZFC set theories.

Mistakes to the contrary
are wrong and/or under-informed.