Re: Replacement of Cardinality

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.

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You need an existence proof [...]
BEFORE stating a/the proper definition.

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Proving that [a unique] mimsy borogove exist[s]
before defining [the] mimsy borogove
seems like a pretty steep hill to climb.

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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.

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Fuck you, asshole. Want't to be the the next crank in sci.math? (After all the other cranks have left?)

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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)