Sujet : Re: Replacement of Cardinality
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.logic sci.mathDate : 16. Aug 2024, 00:24:47
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v9m2nv$14adg$3@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
User-Agent : Mozilla Thunderbird
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.
Re: Replacement of Cardinality
Re: Replacement of Cardinality