9.5.2. Set S with Single 1

Try these first

1. 1.

   Define cardinality in your own words.

   Hint

   Think about how many elements can fit in the set.

2. 2.

   What is an injective function?

   Hint

   Consider the idea of pairing items uniquely.

3. 3.

   What does cardinality measure?

   • Size of a set
   • Quality of a set
   • Type of elements

   Hint

   Think about what you are counting.

4. 4.

   Is it possible for an infinite set to have a cardinality less than א₀?

   • True
   • False

   Hint

   Look back at the definitions of infinite sets.

5. 5.

   Prove that the union of two countably infinite sets is countably infinite with an example.

   Hint

   Think about merging two sequences while maintaining order.

6. 6.

   Explain why a subset of positive integers cannot be both finite and uncountably infinite.

   Hint

   Review definitions of finite and infinite sets.