3.8. Set of Integers

Try these first

1. 1.

   What is the cardinality of the set {A, B, C}?

   Hint

   Count the number of elements in the set.

2. 2.

   Is the set of even numbers countable?

   Hint

   Think about how we can list the even numbers.

3. 3.

   What is a bijection?

   • A one-to-one function
   • A function that repeats elements
   • Any function

   Hint

   Think about the characteristics that define a bijection.

4. 4.

   Is the set of integers countable?

   • True
   • False

   Hint

   Consider the way integers can be sequenced.

5. 5.

   Prove that the set of all even integers is countable by constructing a bijection.

   Hint

   Use the definition of bijection you have learned.

6. 6.

   Determine whether the set of all subsets of natural numbers is countable or uncountable.

   Hint

   Think about the implications of matching elements to subsets.