Path: ...!Xl.tags.giganews.com!local-2.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 15 Sep 2024 21:52:10 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (repleteness)
Newsgroups: sci.math
References: <vb4rde$22fb4$2@solani.org> <vbnuqq$2it4a$2@dont-email.me>
 <vbp9dk$2u3sh$1@dont-email.me> <vbq4ve$31fu6$10@dont-email.me>
 <fd09e9afa6b0c3041b90c5d788681bb2c92f9d2e@i2pn2.org>
 <vbs9v8$3l368$3@dont-email.me>
 <405557f7289631d63264c712d137244c940b9926@i2pn2.org>
 <vbsroa$3mvi7$2@dont-email.me> <vbt0fs$3pr1d$1@dont-email.me>
 <vbt15n$3qapk$1@dont-email.me> <btbO__HYVIMPfoOcmXp4_whV8-8@jntp>
 <vbums6$8kdn$1@dont-email.me> <vbv9i7$bpjh$2@dont-email.me>
 <13c08e96ad635f8142b38d89863a80caf17a32a8@i2pn2.org>
 <vc1mfe$u3ec$2@dont-email.me>
 <4faa63d0ff8c163f01a38736aeb5732184218a29@i2pn2.org>
 <vc1uu8$u3ec$9@dont-email.me> <vc2gfb$130uk$1@dont-email.me>
 <mrednT-A88H9JHj7nZ2dnZfqn_ednZ2d@giganews.com>
 <y8idnRDAGsRvm3r7nZ2dnZfqnPGdnZ2d@giganews.com>
 <vc77he$29vl8$1@dont-email.me>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 15 Sep 2024 14:52:14 -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: <vc77he$29vl8$1@dont-email.me>
Content-Type: text/plain; charset=iso-8859-15; format=flowed
Content-Transfer-Encoding: 7bit
Message-ID: <7-ycnVjnAIKXynr7nZ2dnZfqn_qdnZ2d@giganews.com>
Lines: 86
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-iSyxItP+ZfPYM0rY9h4WCfIVMeLouEtPlLD5woBzWTwPftq+Z+LOK7PgnNjNhK1KzxfSz1PY/8c2IHz!FdUFyVEtrArdT/btPOSNxsFT8l1gJoQrUf0R8kE5lIEjQF+x11htLKYQ7kQk9r8m58/i64qs2FRM
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: 5206

On 09/15/2024 11:03 AM, FromTheRafters wrote:
> After serious thinking Ross Finlayson wrote :
>> On 09/14/2024 09:27 AM, Ross Finlayson wrote:
>>> On 09/13/2024 04:05 PM, FromTheRafters wrote:
>>>> WM explained :
>>>>> On 13.09.2024 17:52, Richard Damon wrote:
>>>>>> On 9/13/24 11:41 AM, WM wrote:
>>>>>
>>>>>>> Between [0, 1] and (0, 1] there is nothing, there is not a spot or
>>>>>>> point of the interval.
>>>>>>>
>>>>>> But that doesn't mean there is a lowest most point in (0, 1] as any
>>>>>> point you might want to call it will have another point between  it
>>>>>> and 0.
>>>>>
>>>>> I will not call any point but consider all points. There is no point
>>>>> smaller than all points in the open interval but a smallest one. Only
>>>>> 0 is smaller than all.
>>>>>>
>>>>>> Note, I said between the point your THINK is the first, there is no
>>>>>> such point, and thus you are agreeing to that fact.
>>>>>>
>>>>>> You can only have a first point in the open interval if the interval
>>>>>> has only a finite number of points,
>>>>>
>>>>> No, that is your big mistake. In the interval [0, 1] there is a point
>>>>> next to 0 and a point next to 1, and infinitely many are beteen them.
>>>>
>>>> Define 'next' in this context.
>>>
>>> The context is "continuous domains",
>>> there are multiple models of continuous domains,
>>> one of them is "iota-values" or "line-reals",
>>> which is a model of a contiguity so fine as
>>> a model of continuity, where it's, "EF(1)".
>>>
>>> Of course, the models of continuous domains are
>>> distinct as with regards to their definitions of
>>> continuity and completeness of operations, so
>>> it entails a bit of book-keeping to keep things.
>>>
>>> Oh, you don't have one of those, ..., well, you
>>> can always look to Aristotle, who has at least
>>> two, and Zeno's always looking for how to arrive
>>> at not being a fool, then fast-forward to Bishop
>>> and Cheng who constructively go about making it
>>> so, and for topology there's Vickers who helps
>>> reflect that in topology there are various topologies
>>> not necessarily the standard open topology, in case
>>> you're thorough about these matters and want to
>>> help square away various models of continuity,
>>> continuous domains, continuous topologies their
>>> own first and final, Cantor space, and law(s) of
>>> large numbers.
>>>
>>>
>>
>> "What, no witty rejoinder?"
>
> What you said has no relation to the 'nextness' of elements in discrete
> sets. What is 'next' to Pi+2 in the reals?

In the, "hyper-reals", it's its neighbors,
in the line-reals, put's previous and next,
in the field-reals, there's none,
and in the signal-reals, there's nothing.

Or, you know, "noise".

Of course the hyper-reals are said to be only
a "conservative" meaning "meaningless" extension
to the standards, so, only the line-reals say
anything about it at all.

Except nothing, ....


I wonder what you think of something like Hilbert's
"postulate of continuity" for geometry, as with
regards to that in the course-of-passage of
the growth of a continuous quantity, it encounters,
in order, each of the points in the line.

Just ignore it?