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Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a countably finite set.
💡 Hint: Think about a set you can count entirely—like a box of candies.
Question 2
Easy
Is the set of all even numbers countable?
💡 Hint: Consider how you can list them.
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
Which of the following is a countably finite set?
- Set of all positive integers
- Set of continents
- Set of all real numbers
💡 Hint: Think of how many continents exist.
Question 2
True or False: The set of all prime numbers is uncountable.
- True
- False
💡 Hint: Recall that primes can be listed as 2, 3, 5, 7, ...
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the set of all even integers is countably infinite.
💡 Hint: Show that every positive integer has a unique even counterpart.
Question 2
Explain Cantor’s diagonal argument and how it demonstrates that the reals are uncountable.
💡 Hint: Focus on the construction of a new number that differs from any given entry in the list.
Challenge and get performance evaluation