Re: Why? [was Re: Cantor`s powerset theorem is false?]

Daryl McCullough wrote:
....
My claim is that for any computable real r you pick, there will
be a natural number n such that the nth bit of r differs from
the nth bit of the randomly generated real. I can't prove this
claim, but I can certainly give you empirical evidence in its
favor.
....

Coming at this from a computer science direction, I have another problem
with bringing the issue of "computability" into the foundations of set
theory.

At least as taught in CS classes, theory of computation is based on set
theory - we assume we know what sets are, that the natural numbers is a
valid set, that power sets exist, that given a set S and a property P,
it is meaningful to talk about the subset of S whose elements all have
property P, etc.

If set theory is going to depend on computability, theory of computation
cannot simply depend on set theory. The two have to be built up together.

Has that been done?

Patricia
.