3.6. Examples of Countably Finite Sets

Try these first

1. 1.

   What is a countable set?

   Hint

   Think about the definition used in determining if a set is countable.

2. 2.

   Give an example of a finite countable set.

   Hint

   Consider a set with a limited number of elements.

3. 3.

   What defines a countably infinite set?

   • It is finite
   • It has a bijection with positive integers
   • It has no elements

   Hint

   Remember the characteristics of countable sets.

4. 4.

   Is the set of integers countable?

   • True
   • False

   Hint

   Think about how you would list both integers and positives.

5. 5.

   Demonstrate a bijection between the set of natural numbers and the set of rational numbers.

   Hint

   Consider how to systematically list all possible fractions.

6. 6.

   Can you create a map for the relation between the set of all integers and the set of even integers?

   Hint

   Think about how one integer corresponds to one even integer.