What is the total number of different sets of natural numbers?

Question

I read that the there are uncountably many different sets of natural numbers. How can you prove that?

possible duplicate of Is the power set of the natural numbers countable? not to mention http://math.stackexchange.com/questions/61926/is-the-class-of-subsets-of-integers-countably-infinite — Gerry Myerson, Aug 08 '13 at 09:12

score 3 · Accepted Answer · answered Aug 08 '13 at 09:09

3

It is an immediate consequence of Cantor's Theorem, which is proved here.

answered Aug 08 '13 at 09:09

1 Answers1