1. The problem statement, all variables and given/known data P(B) refers to the collection of all subsets of B. Given a set B, a subset A of P(B) is called an antichain if no element of A is a subset of any other element of A. Does P(N) contain an uncountable antichain？ 2. Relevant equations 3. The attempt at a solution If I can build a bijective map between an antichain of P(N) and another set of known cardinality, then I will be able to know if the antichain is uncountable. Sets I know that are uncountable: R, sequences of 0's and 1's. Is it one of these two? Sorry I'm not able to do much with this problem. Any help is appreciated.