Re: Replacement of Cardinality

Am 16.08.2024 um 01:16 schrieb Moebius:

Am 16.08.2024 um 00:51 schrieb Jim Burns:
 

Half or more of my proofs to WM say
"Assume otherwise... However... Contradiction."

 Yeah, to be precise: a proof by contradiction assumes a STATEMENT/CLAIM and etc.

But maybe I'm crazy.

 No, you aren't, I guess (or hope).
 

[nonsense deleted]

Hint: If "√2" is not defined, the "statement" (rather expression)
      √2 is irrational
is not a meanigful statement (i.e. mathematical claim). (Got it?)
What you (most certainly) mean is:
      There is no rational number x such that x^2 = 2.
On the ohter hand, in the context of the real numbers we usually have defined "√2" (namely as the real number x > 0 such that x^2 = 2). Hence in this context we may claim
      √2 is irrational [i.e. not a rational number]
AND actually prove this claim.
Hope this helps.