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On 8/8/2024 2:56 PM, FromTheRafters wrote:OOPS!!! God damn it! I meant (1/0) here... damn it! Sorry.Chris M. Thomasson has brought this to us ::^) Depends on your path... ;^) Going from 1 to 0, or 0 to 1.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 :>
>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.
The first unit fraction is 1/1, there is no last one...
... or there is a last one but no first one.
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)->...->(0)
(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... :^)
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