Re: An uncountable countable set

MoeBlee wrote:
Albrecht wrote:
There is no relevance in which system the axiom is found.
E.g. the Axiom A: "Axiom A is wrong", is self contradicting, regardless
of which other axioms are used, I think. The same holds for the axiom
of infinity.

You miss the point. Since you've not shown any contradiction in set
theory, whatever contradiction you claim to have found must be a
contradiction between set theory and something else outside of set
theory. But if you can't articulate that something else as a
mathematical formula, then no one much cares that set theory conflicts
with your not mathematically articulated principles.

Hi MoeBlee - How are you?

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

and

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

(1) is trivially inductively provable.
(2)and (3) are from transfinitology.


So I take it from your response that you don't have a set of axioms for
your mathematics. So I wonder how you expect people to evaluate whether
something is or is not a theorem of your mathematics.

Can you evaluate the relationship between the above three statements?


MoeBlee


Thanx,

Tony
.

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