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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is cardinality?
💡 Hint: Think about how we count items.
Question 2
Easy
Give an example of a countably infinite set.
💡 Hint: Can you list numbers sequentially starting from one?
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 does the Schröder-Bernstein theorem establish?
- That every set has the same cardinality
- That two sets have the same cardinality if both have injective mappings
- That uncountable sets cannot be defined
💡 Hint: Recall if injective mapping implies equality in size of sets.
Question 2
Is the intersection of two uncountable sets always uncountable?
- True
- False
💡 Hint: Consider the examples of different types of sets.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the union of a countably infinite number of countable sets remains countable.
💡 Hint: Focus on how indices can dictate ordering.
Question 2
Given two uncountable sets, describe how their intersection can ever be countable.
💡 Hint: Assess the boundaries set by each uniqueness.
Challenge and get performance evaluation