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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a countable set?
💡 Hint: Think of sets that can be listed.
Question 2
Easy
Give an example of a Cartesian product of two finite sets.
💡 Hint: Consider pairing elements.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
Is there an infinite number of pairs in ℤ × ℤ?
- True
- False
💡 Hint: Consider how many integers exist.
Question 2
How does the enumeration process of ℤ × ℤ begin?
- (0
- 0)
- (1
- 1)
- (1
- 0)
💡 Hint: Remember where we start counting from.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Design a method to prove that the Cartesian product of two countably infinite sets is also countably infinite.
💡 Hint: Think about combining the sequences without omitting any element.
Question 2
How would you determine the 15th pair in the enumeration of ℤ × ℤ?
💡 Hint: Examine the systematic pattern in listing pairs.
Challenge and get performance evaluation