(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: The antichain of a set

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