Re: An uncountable countable set

Tony Orlow wrote:
Set theory contradicts with:

(1) E y e N, A x>y, x< 2*x < x^2 < 2^x (y=2)

because:

(2) A y e N, aleph_0>y

I don't know what you intend '<' to stand for. For the domination
relation? The less than relation on ordinals?

I don't know what is meant by '(y=2)' in the larger formula.

and

(3) aleph_0/2 = aleph_0 = aleph_0^2 < 2^aleph_0

(1) is trivially inductively provable.

Do you mean (1) is a theorem of set theory, or do you mean it is
provable that (1) is the negation of a theorem of set theory?

(2)and (3) are from transfinitology.

What is transfinitology? What is the definition (and in what theory is
this definition?) of '/' where w (omega) is in the numerator?

MoeBlee

.

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