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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Fri, 16 Aug 2024 06:08:19 -0400
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on 8/15/2024, Chris M. Thomasson supposed :
> On 8/15/2024 3:59 PM, Moebius wrote:
>> Am 16.08.2024 um 00:51 schrieb Jim Burns:
>>> On 8/15/2024 3:37 PM, Moebius wrote:
>>>> Am 15.08.2024 um 21:28 schrieb Jim Burns:
>>>
>>>>> Defining ⅟? to be the smallest unit fraction
>>>>> isn't a claim that ⅟? exists.
>>>>
>>>> You need an existence proof [...]
>>>> BEFORE stating a/the proper definition.
>>>
>>> Proving that [a unique] mimsy borogove exist[s]
>>> before defining [the] mimsy borogove
>>> seems like a pretty steep hill to climb.
>> 
>> No mater what you think, in math we HAVE TO climb this hill, and we do.
>> 
>>> That's a hill which I doubt we need to climb.
>> 
>> Fuck you, asshole. Want't to be the the next crank in sci.math? (After all 
>> the other cranks have left?)
>
> Wrt sqrt(2), afaict anytime we create a unit square, we have the sqrt(2) in 
> all of its irrational infinite glory as a diagonal.

Every time we 'create' a circle we have Pi as a transcendental number 
too. That is not the same as having a mathematical system to work with 
irrational and/or transcendental numbers in Q, so we imagined R to fill 
the 'gaps' in Q and we're golden.