Re: Replacement of Cardinality

On 8/8/2024 2:56 PM, FromTheRafters wrote:

Chris M. Thomasson has brought this to us :

On 8/8/2024 3:30 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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The first unit fraction is 1/1, there is no last one...

 ... or there is a last one but no first one.

:^) Depends on your path... ;^) Going from 1 to 0, or 0 to 1.
So:
(0/1)->...->(1/1)
(0/1) is not a unit fraction so there is no first one in this context.
However, going from:
(1/1)->...->(1/0)
There is a first one in this context.
I generally consider (1/1) to be the first unit fraction.
The main point is that there is no smallest unit fraction and there is no largest natural number... :^)