Path: ...!Xl.tags.giganews.com!local-4.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Wed, 23 Oct 2024 00:49:31 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Newsgroups: sci.math
References: <vb4rde$22fb4$2@solani.org>
 <68b8be64-7fe8-47e7-a991-7adf14713af5@att.net> <vejmkm$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>
 <9Jmcnd4bjJjX_on6nZ2dnZfqnPGdnZ2d@giganews.com>
 <48d0e1b1-f12a-4612-8eb1-52a89b8493d0@att.net>
 <v8WcncPe1YKKrYj6nZ2dnZfqnPidnZ2d@giganews.com>
 <9d33ab3b-aacc-4469-949d-70d4e16579c5@att.net>
 <M7Ccnb_UZYiuA4j6nZ2dnZfqn_SdnZ2d@giganews.com>
 <897d83c5-f2a5-42b5-b8ee-e007e5c8e289@att.net>
 <FnCdnbPrSYAjBYv6nZ2dnZfqn_SdnZ2d@giganews.com>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Tue, 22 Oct 2024 17:49:55 -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: <FnCdnbPrSYAjBYv6nZ2dnZfqn_SdnZ2d@giganews.com>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 7bit
Message-ID: <KcqdnSt8s_mG1YX6nZ2dnZfqn_EAAAAA@giganews.com>
Lines: 105
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-AT5PJU0zod26BKhUVppsetVowfigtDJwDJWJ60qolN+CT+UJzgxqIPiRk2TIjTQUH1tFpTv85m0h5H8!TiNMOMMeucVtGVx5wN0zPwaY3LjvFUFfBWQpFhmCQc3gwD+61aYBYQz+p+QLS4qkoMOzrCDlHe8k!eA==
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: 5798

On 10/21/2024 11:09 AM, Ross Finlayson wrote:
> On 10/21/2024 09:21 AM, Jim Burns wrote:
>> On 10/20/2024 8:20 PM, Ross Finlayson wrote:
>>> On 10/20/2024 11:33 AM, Jim Burns wrote:
>>>> On 10/20/2024 12:30 PM, Ross Finlayson wrote:
>>>>> On 10/20/2024 06:36 AM, Jim Burns wrote:
>>
>>>>>> Is there some sort of protocol
>>>>>> which you (RF) recognize
>>>>>> in order to talk about a thing
>>>>>> and not.talk about things not.that?
>>>>>
>>>>> Here there's freedom of speech it one of
>>>>> what we call constitutional liberties,
>>>>
>>>> I take your answer to mean
>>>> "no, there is no such protocol".
>>>>
>>>> Surely,
>>>> with your degree in mathematics,
>>>> you understand that
>>>> you are depriving yourself of
>>>> the use of a powerful tool.
>>
>>> Au contraire, to the contrary,
>>> I proffer that
>>> extending the relevant domain while keeping it
>>> a completely connected relevant domain
>>> _is_ a most proper and surmounting
>>> improvement of the discourse,
>>> to include the wider considerations of
>>> a topic in the _foundations_ of the theory,
>>> not merely a single theorem
>>> under a microscope.
>>
>> Microscopes and
>> finite sequences of only not.first.false claims
>> are powerful tools.
>>
>> Do you refuse to use microscopes or
>> knowledge from microscopes?
>>
>>> Anyways you still haven't picked "anti and only".
>>
>> I vaguely recall that
>> you (RF) made some incorrect claims about
>> Cantor's  argument from anti.diagonals,
>> and you asked for my participation in some way.
>> Could you refresh my memory? TIA.
>>
>>
>
> I'm not much inclined since you ignored it
> about ten times because what it is is that
> it uses the same reasoning for the anti-diagonal
> result that there are no Cartesian bijections
> between domains of different cardinalities to
> show that the non-Cartesian function with
> only one diagonal the only-diagonal exists
> and is not so precluded.
>
> Yet, I'm inclined because it's always true,
> and in the case that you really have these
> recurring gaps in your memory, that over the
> past several and more months there's been
> at least ten mentions of this here on sci.math.
>
> We were discussing Zeno and mathematical continuity
> and I kept pointing out you were missing out on
> the fuller dialectic and indeed that there are
> plain inductive arguments to spoil your plain
> inductive argument, thus _requiring_ a fuller
> deductive argument and explaining how indeed
> the "infinite limit" does reach the sum, and
> as with regards to the "continuum limit" of
> functions, that in the continuum limit the
> line integral exists and in the continuum limit
> these line-reals exist, then I pointed out that
> the very same reasoning of the anti-diagonal
> argument itself, which I sort of ignore because
> it's not constructivist usually in the sense of
> imputing what it doesn't and contradicting itself,
> that: there's correspondingly an only-diagonal
> argument that line-reals result from a function
> that has a discrete range and continuous, and
> countable, domain.
>
> Then I suggested that I would put anti-diagonal
> in one fist, only-diagonal in the other, then
> hide them behind my back and perhaps exchange
> them, then that you get to pick.
>
> You get to pick, was the idea, then I laughed
> and said that I had put them together, so,
> you get both or none.
>
> "You" here meaning anybody, ..., because it's
> a mathematical statement so is the same for anyone.
>
>
>

Or, you know, don't, ....