9.1.2. Question 2

Try these first

1. 1.

   What is cardinality?

   Hint

   Think about how you count elements in set S.

2. 2.

   Define injective mapping.

   Hint

   Recall the relationship between sets A and B.

3. 3.

   What does cardinality measure?

   • The type of elements in a set
   • Number of elements in a set
   • Set operations

   Hint

   Think about what cardinality actually tells us.

4. 4.

   Is an infinite subset of the positive integers always countably infinite?

   • True
   • False

   Hint

   Remember how sequences work in infinite sets.

5. 5.

   Construct a proof that demonstrates there can be no infinite set A with cardinality less than א₀, detailing the implications of the defined claims. Use examples to illustrate.

   Hint

   Ensure you follow the logical structure presented in the section's proof.

6. 6.

   Provide an example of two different infinite sets that have the same cardinality, and explain how you would show they are countably infinite.

   Hint

   Focus on the mapping process and how it confirms set equality.