In 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:

We usually denote this set by A = 2^N.

a. Show that 2^N is in one-to-one correspondence with the set of all (infinite) binary sequences:

b. Show that C is in one-to-one correspondence with [0, 1].

From (a) and (b) we conclude that the set 2^N is uncountable.

Transcribed Image Text:

A = {B: BCN}.