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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Mon, 12 Aug 2024 13:23:21 -0400
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On 8/12/24 9:50 AM, WM wrote:
> Le 11/08/2024 à 19:56, Jim Burns a écrit :
>> On 8/11/2024 8:29 AM, WM wrote:
> 
>>>> What causes an exception: nₓ ∈ ℕ without ⅟(nₓ+1) ?
>>>
>>> The end of the positivee axis.
>>
>>>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
>>
>> ∀n ∈ ℕ: 1/n > 1/(n+1) > 0
> 
> If 1/(n+1) exists.

Which, by the definition of the Natural Numbers, it does.

Of course, if your logic doesn't actually allow the Natural Numbers to 
exist as a set, then you shouldn't be using it.

>>
>> Each positive unit fraction is not
>> the first positive unit fraction.
>>
>> What causes an exception: nₓ ∈ ℕ:
>> ⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?
> 
> The end of the positive axis.

Which, by the definition of the Natural Numbers, doesn't exist.

Of course, if your logic doesn't actually allow the Natural Numbers to 
exist as a set, then you shouldn't be using it.

Since it is clear that you logic can't handle the Natuarl Numbers, you 
are just al Number, you use of them just shows you don't mind using 
broken logic.

> 
> Regards, WM
> 
>