Re: Replacement of Cardinality

Am 09.08.2024 um 05:34 schrieb Jim Burns:

On 8/8/2024 5:56 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 :

 

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)."

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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 [...]  element.

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The first unit fraction is 1/1, there is no last one...

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

Which is the case in respect to the usual < defined on ÌR.
1/1 is the <-largest/last unit fraction and there is no <-smallst/first unit fraction. Rather simple facts. Expect in Mückenhausen of course,