Practice - Countable and Uncountable Sets
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Practice Questions
Test your understanding with targeted questions
What is the cardinality of the set X = {Alice, Bob}?
💡 Hint: Count the number of names in the set.
Is the set Y = {1, 2, 3, 4} countable?
💡 Hint: Check if it's possible to list elements.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a countable set?
💡 Hint: Think about the definitions discussed regarding countable sets.
True or False: The set of all real numbers is countable.
💡 Hint: Consider Cantor’s diagonal argument!
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Challenge Problems
Push your limits with advanced challenges
Show that the set of all even integers is countable by constructing a bijection with positive integers.
💡 Hint: Use the formula relating each even integer to positive integers.
Explain why the interval [0, 1] contains uncountably many numbers.
💡 Hint: Reflect back on concepts involving real numbers and enumeration.
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Reference links
Supplementary resources to enhance your learning experience.