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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality (infinite middle)
Date: Fri, 09 Aug 2024 18:22:08 -0400
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Ross Finlayson used his keyboard to write :
> On 08/09/2024 03:25 AM, FromTheRafters wrote:
>> Ross Finlayson explained :
>>> On 08/08/2024 03:30 AM, FromTheRafters wrote:
>>>> on 8/8/2024, WM supposed :
>>>>> Le 08/08/2024 � 00:17, Moebius a �crit :
>>>>>
>>>>>> Actually, his "thinking process" is simple:
>>>>>>
>>>>>> "Since there is a gap (space) between adjacent unit fractions and all
>>>>>> unit fractions are in the interval (0, 1], there must be FINITELY
>>>>>> MANY of them (i.e. a first/smallest one)."
>>>>>
>>>>> No, that is nonsense. There are not finitely many unit fractions.
>>>>
>>>> Then stop assuming that there is a first and last element.
>>>
>>> Of course, you can start with a first and last element,
>>> then make infinitely-many in the middle.
>>>
>>> 0 ... ( ... infinitely-many ... ) ... infinity
>>
>> Sometimes you are as bad as he is. :)
>
>
> I seem to recall being an eighth-grader, and representing
> my entire region in, "MathCounts", there's a nice picture
> of me as was in the newspaper with the background of all
> the stacks of the library.
>
> It didn't seem un-usual to be a National Merit Finalist.
> There were at least seven in my class.
>
> Or, "das ist ein Zwerg, hier ist ein Hengst".
>
> I have a mathematics degree.
>
> Mostly though I've been studying foundations for three decades,
> looking for one good theory, "A Theory".
>
> A good mathematical and natural science theory -
> there's already a holistic approach to the super-scientific.
> I.e., one hopes it may so be, one hopes it may so be.
>
> I think WM is just another linguist's chat-bot to burden
> and make disparaged the commons. He or it has had plenty
> of time to take strong arguments and their results offered
> here instead of humping the same stump.
>
>
> Anyways, I'm only interested in one theory,
> yet it has to be the entire thing, "the theory", "A Theory".
>
> Of course, it's both paleo-classical and post-modern,
> built on the giant scholars, and bearing them up.
>
> "a tower of rain"
>
> So, infinity shows up a lot in mathematics and
> continuity is very central and primary, in it.
>
> Then, drawing the ends apart with infinite in the middle,
> has a little extra work and book-keeping to begin instead
> of a usual "next", yet it well expresses any matters of
> the "bounded", for example, in any matters of the "unbounded".
>
> Or, where do you think you're counting, to?

I'm not really stuck on counting for this. I just imagine a number line 
of infinitely many integers as a zero ended object. With a starting 
point and no ending point I have an infinite ray (one ended) object, 
with a starting point and an ending point I have a line segment (two 
ended) object.