3.3. Definition of Countable Sets

Try these first

1. 1.

   Define a countable set.

   Hint

   Think about the characteristics of finite sets.

2. 2.

   Is the set of prime numbers countable?

   Hint

   Can you list them in order?

3. 3.

   What defines a countable set?

   • It must have a finite number of elements.
   • It can be either finite or have the same cardinality as positive integers.
   • It cannot have an infinite number of elements.

   Hint

   Remember the definition of countability.

4. 4.

   Which set is not countable?

   • The set of natural numbers.
   • The set of real numbers.
   • The set of odd numbers.

   Hint

   Think about how many numbers are between any two integers.

5. 5.

   Determine if the set of all even integers is countable and justify your answer.

   Hint

   Consider the way they pair with positive integers.

6. 6.

   Show whether the set of all subsets of natural numbers is countable.

   Hint

   Think about how many subsets can exist versus elements.