Practice - Countably Finite Sets and Countably Infinite Sets
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Practice Questions
Test your understanding with targeted questions
Define a countably finite set.
💡 Hint: Think about a set you can count entirely—like a box of candies.
Is the set of all even numbers countable?
💡 Hint: Consider how you can list them.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which of the following is a countably finite set?
💡 Hint: Think of how many continents exist.
True or False: The set of all prime numbers is uncountable.
💡 Hint: Recall that primes can be listed as 2, 3, 5, 7, ...
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Challenge Problems
Push your limits with advanced challenges
Prove that the set of all even integers is countably infinite.
💡 Hint: Show that every positive integer has a unique even counterpart.
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.
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