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Am 08.08.2024 um 22:36 schrieb Chris M. Thomasson:Yup. Instead if using first, I should say largest... Any better?On 8/8/2024 3:30 AM, FromTheRafters wrote:Nope. We are using the usual order < defined on IR to determine if there is a first (smallest) / last (largest) unit fraction.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 [i.e. smallest] element.
The first unit fraction is 1/1, there is no last one...
So there is no first/smallest unit fraction and there is a last/largest unit farction (namely 1/1), in respect to <.
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