Path: ...!Xl.tags.giganews.com!local-1.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 20 Oct 2024 01:56:26 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Newsgroups: sci.math
References: <vb4rde$22fb4$2@solani.org> <ve5u2i$2jobg$4@dont-email.me>
 <ve6329$19d5$1@news.muc.de> <ve64kl$2m0nm$4@dont-email.me>
 <ve66f3$19d5$2@news.muc.de> <ve683o$6c2o$1@solani.org>
 <09d9f0df-b1bb-42a7-af9b-890bfbcfc581@att.net>
 <b0fa9a1c-8375-4523-a15e-65789688660e@tha.de>
 <3f63bc22-83b2-4d56-9837-849551170c77@att.net>
 <50ac7044-f8c1-47d9-947f-9fa6044e1848@tha.de>
 <68b8be64-7fe8-47e7-a991-7adf14713af5@att.net> <vejmkm$e069$1@solani.org>
 <eb21591a-a60a-4baf-bdbd-afef2a69c230@att.net> <vejte9$e3ds$1@solani.org>
 <53460f91-4542-4a92-bc4b-833c2ad61e52@att.net> <ventec$255vi$2@dont-email.me>
 <venunr$2533b$4@dont-email.me> <29ce40e9-f18a-44d4-84d9-23e587cf9dea@att.net>
 <veor6u$2asus$1@dont-email.me> <2b6f9104-a927-49ee-9cf0-6ee3f82edc23@att.net>
 <verkkk$2r6kk$1@dont-email.me> <22f95ff7-c361-4d8a-943c-1df76abb98cc@att.net>
 <vevpsl$3pi3s$2@dont-email.me> <ed1862ff-3679-4175-bb25-c317be9713b2@att.net>
 <vf0t7i$3v3cv$5@dont-email.me> <9c55eda1-bb24-44ae-9158-2a3b354170cd@att.net>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sat, 19 Oct 2024 18:56:45 -0700
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: <9c55eda1-bb24-44ae-9158-2a3b354170cd@att.net>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Message-ID: <9Jmcnd4bjJjX_on6nZ2dnZfqnPGdnZ2d@giganews.com>
Lines: 106
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-MMHxrZgm3qH7bIjQStXqD2Rib/wpb9mmH9Fvic33KpGAXG/KHCUmTJY4yDhwhePDGNmjtqHC9atynBv!iuhROdosBQawhFJVYFWhz+Mdbs6aVBcsdWCaKABhSXH7Au5HkOus1Pq3BlTCIvDp+XjFmTu8zoUj
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: 4998

On 10/19/2024 03:54 PM, Jim Burns wrote:
> On 10/19/2024 2:19 PM, WM wrote:
>> On 19.10.2024 18:04, Jim Burns wrote:
>>> On 10/19/2024 4:16 AM, WM wrote:
>
>>>> What you call a "set of finite ordinals" is
>>>> not a set
>>>> but a potentially infinite collection.
>>>
>>> There is a general rule not open to further discussion:
>>> Finite sets aren't potentially infinite collections.
>>
>> Potentially infinite collections are
>> finite sets open to change.
>
> That makes it easy.
>
> No sets are open to change.
> No sets are (your) potentially infinite,
> No finite sets are potentially infinite.
>
> The rule stands.
>
>>>> Proof:
>>>> If you double all your finite ordinals
>>>> you obtain only finite ordinals again,
>>>
>>> Yes.
>>>
>>>> although the covered interval is
>>>> twice as large as the original interval
>>>> covered by "all" your finite ordinals.
>>>
>>> No.
>>> The least.upper.bound of finites is ω
>>> The least.upper.bound of doubled finites is ω
>>
>> Doubling halves the density and doubles the interval,
>> creating numbers which had not been doubled.
>> 2n > n does not fail for any natural number.
>
>>> The least.upper.bound of finites is ω
>
> What ω is
> is such that
> k < ω  ⇔  k is a finite ordinal.
>
> No k exists such that
> k is a finite and k+1 > k is not a finite.
>
> No k exists such that
> k is an upper.bound of the finites.
>
> ω is but anything prior to ω isn't
> an upper.bound of the finites.
>
> ω is the least.upper.bound of the finites.
>
>>> The least.upper.bound of doubled finites is ω
>
> A doubled finite is finite.
>
> No k exists such that
> 2⋅k is a finite and 2⋅k+2 > 2⋅k is not a finite.
>
> No k exists such that
> 2⋅k is an upper.bound of the doubled finites.
>
> ω is but anything prior to ω isn't
> an upper.bound of the doubled finites.
>
> ω is the least.upper.bound of the doubled finites.
>
>



Isn't mathematics true?



You still haven't picked "anti or only" diagonal,
i.e. since they're together that's neither.

I mean, I see where you're going with that,
yet also I can assure you
it doesn't get all the way there.

Yet you trust Russell that's he's been to the mountain, ....

The omega is usually called a fixed-point besides
being a limit ordinal, also it's called a compactification
or one-point compactification of the integers for
the most usual sort of idea of a non-standard countable
model of integers with exactly one infinite member.

(This is not the usual Tipler's "omega-point", say,
which is not of so much relevant here though it
reflects convergence to a point at infinity as much
as it does mutual divergence, to infinity.)

Clearly it's not merely exactly a finite member, say, ....