9.5.1. Set S with Recurring 1s

Try these first

1. 1.

   Define cardinality in your own words.

   Hint

   Think of the term as a way to measure the size.

2. 2.

   What is an injective mapping?

   Hint

   Focus on how elements correspond to one another.

3. 3.

   What does cardinality measure?

   • The shape of a set
   • The size of a set
   • The color of a set

   Hint

   Think about what it means to compare sizes.

4. 4.

   True or False: Every countable set is finite.

   • True
   • False

   Hint

   Remember the examples discussed for infinite sets.

5. 5.

   Given a set of all real numbers, can you extract a countably infinite subset?

   Hint

   Think about the properties of rational numbers!

6. 6.

   Create an example showing the union of any infinite countable sets.

   Hint

   Look at how lists can overlap without losing countability.