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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the cardinality of the set of integers?
💡 Hint: Think about the natural numbers.
Question 2
Easy
Is the set of all real numbers between 0 and 1 countably infinite?
💡 Hint: Consider Cantor's diagonal argument.
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
What is the definition of a countable set?
- A set that has a finite number of elements.
- A set that can be listed in correspondence with natural numbers.
- Any set.
- An infinite set.
💡 Hint: Think about how we can list elements of a set.
Question 2
True or False: The intersection of two uncountable sets is always uncountable.
- True
- False
💡 Hint: Consider overlapping intervals.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
Construct a sequence in which the union of subsets remains countable. Provide an example.
💡 Hint: List down individual subsets and combine interestingly.
Challenge and get performance evaluation