7.1. Introduction to Cardinality

Try these first

1. 1.

   What does cardinality refer to?

   Hint

   Think about how we count elements in a bag.

2. 2.

   If set A has 3 elements, how many elements are in its power set?

   Hint

   Remember the formula for the power set.

3. 3.

   What is the cardinality relationship established by Cantor's theorem?

   • The cardinality of set A is greater than the power set P(A)
   • The cardinality of set A is less than the power set P(A)
   • The cardinality of set A is equal to the power set P(A)

   Hint

   Remember the definition of the power set.

4. 4.

   True or False: The power set of a finite set always contains 2^n elements, where n is the number of elements in that set.

   • True
   • False

   Hint

   Think about the counting of subsets.

5. 5.

   Construct an example of a finite set and calculate its power set, then identify its cardinality.

   Hint

   List all possible subsets to ensure you haven't missed any.

6. 6.

   Explain the significance of Cantor's proof on the concept of different sizes of infinity. Provide a real-world analogy.

   Hint

   Consider how different types of numbers can fill up the number line.