Practice - Set of Real Numbers between 0 and 1
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Practice Questions
Test your understanding with targeted questions
Define a countably infinite set.
💡 Hint: Think about a set you can list or count.
What is an uncountable set?
💡 Hint: Consider whether you can list all elements.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does uncountable mean?
💡 Hint: Consider if you can list out all elements.
True or False: All infinite sets are countable.
💡 Hint: Think about the set of real numbers.
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Challenge Problems
Push your limits with advanced challenges
Construct a set to show that the set of real numbers cannot be counted. Use Cantor's method to illustrate.
💡 Hint: Think about how flipping each digit creates a new, unlisted number.
Using a bijection, explain how the infinite binary strings are related to real numbers between 0 and 1.
💡 Hint: Look at binary representations and their decimal equivalents in the specified interval.
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Reference links
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