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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Wed, 07 Aug 2024 17:16:09 -0400
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WM brought next idea :
> Le 07/08/2024 à 20:15, Moebius a écrit :
>> Am 07.08.2024 um 20:03 schrieb Jim Burns:
>>> On 8/7/2024 8:31 AM, WM wrote:
>> 
>>>> Do you agree that
>>>> all unit fractions with no exception
>>>> have gaps on the real line?
>> 
>> For WM this fact "implies" that there is a first/smallest unit fraction.
>
> Of course. Never two can be added simultaneously to NUF(x)
>> 
>> "∀n ∈ ℕ: 1/n - 1/(n+1) > 0 implies its existence." (WM)
>> 
>> (1) (1/n - 1/(n+1))_(n e IN) is a null sequence
>
> Nevertheless no unit fractions are without gap to their neighbours.

In the rationals.