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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Replacement of Cardinality
Date: Sat, 17 Aug 2024 10:17:28 -0400
Organization: i2pn2 (i2pn.org)
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On 8/17/24 9:30 AM, WM wrote:
> Le 16/08/2024 à 19:54, Jim Burns a écrit :
>> On 8/16/2024 1:00 PM, WM wrote:
> 
>>> Start from x = 0.
>>> The increase cannot be more than 1.
>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
>>
>> Start from x = 0
>> The increase cannot be less than 2
> 
> That violates ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 .
> 
>> ∀ᴿx > 0:  x  >  ⅟nₓ  >  ⅟(nₓ+1)
>> nₓ = ⌊1+⅟x⌋
> 
> That holds only for definable numbers.
> 
> Regards, WM
> 
> 

Which is all of the Rational Numbers, and thus all of the unit fractions.

Thats your problem, you don't seem to know how to definie numbers.