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


William of Ockham wrote:

<snipped>

At exactly what point does
Cantor's proof of the uncountablity of the reals fall down? You said
in another post that the assertion that the power set of N exists is
meaningless. But how? A power set of a set is just a set containing
every subset of the given set. Why is that not meaningful?

Maybe he means that if you dismiss a "set of all sets", then you can't
just assume that P(N) exists or define it into existance. Suppose all
sets can be mapped to a subset of N, then wouldn't P(N) be the "set of
all sets" by definition?

.

Relevant Pages
Quantcast