Which of the sets is larger, (Natural numbers and B_n)?

Question

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This one seems pretty tricky to me atleast

Answer 1

you can make a mapping from {1,..N} to Bn where a number out of first set is mapped on the binairy representation of a n-tuple. Bn ' cardinality is clearly more than the other set.

Answer 2

The set B_n is a slightly different representation of the Power Set (the set of all subsets) of {1, ..., n}. Since you are asking this problem you have probably seen the theorem that that for any set S, |S| < |Powerset(S)|. If not, check out the link below.