Recent content by Edward357

any comments?

Thanks, but I want to do this without CH. I should not need more than plain old ZFC.

For any infinite K, K^n has the same cardinality as K provided n is finite. Then U{K^n : n in N} has a card equal to lK^1 + K^2 + K^3 ... + K^n...l for all natural numbers n. Each K^n has card lKl so this calculation is equivalent to lKl . aleph_0 which equals lKl because lKl is infinite. I...

O.k. If K is an infinite set, then form U K^n for natural numbers n. We know that if card K = lKl, then K^2 has card lKl. We know that for any finite natural number, K^n has cardinality lKl. The union of all K^n is equivalent to lKl + lKl with the operation repeated countably many times...

I know that it is not true that every finite subset of an infinite set has the same cardinality as the infinite set. No finite subset of an infinite set has the same cardinality as the infinite set. The question was about the set of ALL finite subsets of an infinite set.

How do I prove that the set of all finite subsets of an infinite set has the same cardinality as that infinite set?