9.4.1. Set S Definition

Try these first

1. 1.

   Define the term 'cardinality'.

   Hint

   Think about how you count objects in a box.

2. 2.

   What is an injective mapping?

   Hint

   Remember, no two inputs should overlap in their outputs.

3. 3.

   What does the term 'cardinality' refer to?

   • Size of a set
   • A type of set
   • An equation

   Hint

   Consider the number of items in a collection.

4. 4.

   If two sets have injective mappings between them, what can we conclude?

   • True
   • False

   Hint

   Think about the relationships defined by these mappings.

5. 5.

   Create a set of rational numbers between 0 and 1 and prove its cardinality.

   Hint

   Think about how to list all possible fractions fitting that description.

6. 6.

   Prove the intersection of two uncountable sets can be empty.

   Hint

   Visualize how different sets can share no values.