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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Tue, 13 Aug 2024 17:11:53 -0400
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Chris M. Thomasson used his keyboard to write :
> On 8/13/2024 12:13 PM, Chris M. Thomasson wrote:
>> On 8/13/2024 9:07 AM, FromTheRafters wrote:
>>> WM used his keyboard to write :
>>>> Le 12/08/2024 à 19:23, Richard Damon a écrit :
>>>>> On 8/12/24 9:50 AM, WM wrote:
>>>>
>>>>>>> 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.
>>>>
>>>> The end of the positive axis exists.
>>>
>>> Right there where the negative axis begins?
>> 
>> Ahh! Touche. :^D
>> 
>> Well, lets say the real axis, or x axis if you will:
>> 
>> (...)<--(-1)<--(-0+)-->(+1)-->(...)
>> 
>> It's infinitely long... Notice the signed zero? lol. Fair enough?
>> 
>> 
>
> I consider zero to be the origin for any n-ary axes system. For 2d (0, 0), 3d 
> (0, 0, 0) for 4d (0, 0, 0, 0), 5d (0, 0, 0, 0, 0), ect, ect... ;^)

I prefer the unsigned version. Sometimes the set of naturals is called 
the positive integers and the naturals with zero as non-negative 
integers.