Re: Replacement of Cardinality (infinite middle)

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 à 00:17, Moebius a écrit :
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Actually, his "thinking process" is simple:
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"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)."

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No, that is nonsense. There are not finitely many unit fractions.

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Then stop assuming that there is a first and last element.

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Of course, you can start with a first and last element,
then make infinitely-many in the middle.
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0 ... ( ... infinitely-many ... ) ... infinity

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Sometimes you are as bad as he is. :)

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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.
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It didn't seem un-usual to be a National Merit Finalist.
There were at least seven in my class.
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Or, "das ist ein Zwerg, hier ist ein Hengst".
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I have a mathematics degree.
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Mostly though I've been studying foundations for three decades,
looking for one good theory, "A Theory".
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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.
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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.
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Anyways, I'm only interested in one theory,
yet it has to be the entire thing, "the theory", "A Theory".
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Of course, it's both paleo-classical and post-modern,
built on the giant scholars, and bearing them up.
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"a tower of rain"
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So, infinity shows up a lot in mathematics and
continuity is very central and primary, in it.
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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".
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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.