3.2. Cardinality of Infinite Sets

Try these first

1. 1.

   What is the cardinality of the set {A, B, C}?

   Hint

   Count the elements in the set.

2. 2.

   Is the set of all even numbers countable or uncountable?

   Hint

   Can you list the even numbers in a sequence?

3. 3.

   Which symbol denotes the cardinality of countably infinite sets?

   • ℵ₀
   • ∞
   • C

   Hint

   Think about what symbol we learned for countably infinite sets.

4. 4.

   True or False: The set of all integers is uncountable.

   • True
   • False

   Hint

   Remember how we can list integers in a sequence.

5. 5.

   Consider the set of all rational numbers. Determine if it is countably infinite and provide a proof.

   Hint

   Try constructing a diagonal argument to illustrate the listing of rationals.

6. 6.

   What can you infer about the power set of a countably infinite set? Is it countable or uncountable?

   Hint

   Reflect on how many subsets a set has and consider Cantor's argument.