n this problem our goal is to show that sets that are not in the form of intervals may also be uncountable. In particular, consider the set A defined as the set of all subsets of ℕ : A={B:B⊂ℕ}. We usually denote this set by A=2ℕ . Show that 2ℕ is in one-to-one correspondence with the set of all (infinite) binary sequences: C={b1,b2,b3,⋯|bi∈{0,1}}. Show that C is in one-to-one correspondence with [0,1] . From (a) and (b) we conclude that the set 2ℕ is uncountable.