Practice - Union of Sets S
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Practice Questions
Test your understanding with targeted questions
What is the cardinality of the set of integers?
💡 Hint: Think about the natural numbers.
Is the set of all real numbers between 0 and 1 countably infinite?
💡 Hint: Consider Cantor's diagonal argument.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the definition of a countable set?
💡 Hint: Think about how we can list elements of a set.
True or False: The intersection of two uncountable sets is always uncountable.
💡 Hint: Consider overlapping intervals.
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Challenge Problems
Push your limits with advanced challenges
Given two infinite sets, A and B, with A included in B, prove A's cardinality is less than or equal to B.
💡 Hint: Start by demonstrating elements of A can map to B.
Construct a sequence in which the union of subsets remains countable. Provide an example.
💡 Hint: List down individual subsets and combine interestingly.
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Reference links
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