9.2. Claim 1

Try these first

1. 1.

   Define cardinality.

   Hint

   Think about how we measure the size of a collection.

2. 2.

   What is an injective mapping?

   Hint

   Consider how a one-to-one relationship works.

3. 3.

   What does cardinality measure?

   • The size of a set
   • The total number of distinct numbers
   • The frequency of elements in a set

   Hint

   Think about how we define the overall count of items.

4. 4.

   True or False: An injective mapping can map two different inputs to the same output.

   • True
   • False

   Hint

   Reflect on the one-to-one relationship described in definitions.

5. 5.

   Prove that the set of rational numbers is countably infinite.

   Hint

   Structure your list carefully to ensure each fraction is included exactly once.

6. 6.

   Show that removing one element from any infinite set leaves an infinite set.

   Hint

   You can relate it to the counting of elements and their infinite nature.