9.1.1. Question 1

Try these first

1. 1.

   Define cardinality.

   Hint

   Think about what it means to count elements in a collection.

2. 2.

   Give an example of a finite set.

   Hint

   Remember, finite sets have a definite number of elements.

3. 3.

   What is the property of an injective mapping?

   • All elements map to the same element
   • Distinct elements map to distinct elements
   • Elements can overlap

   Hint

   Think about the definitions we discussed regarding functions.

4. 4.

   True or False: The Schroder-Bernstein theorem applies only to finite sets.

   • True
   • False

   Hint

   Recall the definitions provided about the theorem and its applicability.

5. 5.

   Explore the implications of having a set with cardinality less than א_0 and describe properties that would arise from it.

   Hint

   Reflect on how cardinality defines subsets and how numbers can represent mappings.

6. 6.

   Determine whether the set of all rational numbers has the same cardinality as the natural numbers and justify your reasoning.

   Hint

   Think about how you can list rationals similar to how natural numbers are listed.