Solution for Section 7.6 Question 3

3. Two sets have the same cardinality if, and only if, there is a one-to-one correspondence between them. We know that:

• the set of positive integers, Z⁺,  is countable;
• there cannot be a one-to-one correspondence between Z⁺ and  P(Z⁺), by question 2.

Hence the set P(Z⁺) cannot be countable, so it must be uncountable.

Back to Section 7.6