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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Replacement of Cardinality
Date: Tue, 30 Jul 2024 21:31:56 -0400
Organization: i2pn2 (i2pn.org)
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On 7/30/24 1:39 PM, WM wrote:
> Le 30/07/2024 à 03:20, Richard Damon a écrit :
>> On 7/29/24 9:15 AM, WM wrote:
>>> Le 29/07/2024 à 11:01, Mikko a écrit :
>>>
>>>> He also notes that what we have learned from finite quatities does
>>>> not apply to infinity.
>>>
>>> Unit fractions are isolated. They have distances. The function "unit 
>>> fractions between 0 and x" can nowhere grow by more than 1.
>>
>> Unless it just jumps to infinity because it isn't actually correctly 
>> defined.
> 
> It is correctly defined. Try to define the function Number of 
> UnitFractions between 0 and x as you like it but in accordance with 
> mathematics ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
> 
> Regards, WM

And you equation proves that there is no smallest unit fraction as your 
mathematics also says that you statement is equivalent to

∀n ∈ ℕ: 1/n > 1/(n+1) so there does not exist a smallest unit fraction, 
since part of the definition of the Natural numbers is that
∀n ∈ ℕ: there exist n+1 ∈ ℕ