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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Fri, 16 Aug 2024 02:03:26 +0200
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Am 16.08.2024 um 01:39 schrieb Moebius:
> Am 16.08.2024 um 01:35 schrieb Chris M. Thomasson:
>> 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 ⅟𝔊 to be the smallest unit fraction
>>>>>> isn't a claim that ⅟𝔊 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.
> 
> Right. In the context of geometry [...]

Actually, we see/know that there is a "diagonal" of a unit square, but 
its length and and the length 1 are "incommensurable".

See: https://en.wikipedia.org/wiki/Commensurability_(mathematics)