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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is an injective function?
💡 Hint: Think of a one-to-one relationship.
Question 2
Easy
Does the function f(x) = x^2 is injective for positive integers?
💡 Hint: Check if any two inputs lead to the same output.
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 Schroder-Bernstein theorem establish about the cardinalities of sets?
- They can never be equal
- They are equal if both have injective functions
- They are always infinite
💡 Hint: Think back to the conditions required for the theorem.
Question 2
True or False: If |A| ≤ |B|, it necessarily means A is larger than B.
- True
- False
💡 Hint: Refer to the definition of cardinality.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the set of all rational numbers is countably infinite using the concepts from the Schroder-Bernstein theorem.
💡 Hint: Use the structured nature of rational numbers to establish your mappings.
Question 2
Show two sets, one infinite and one finite, and explain how this relates to the application of the Schroder-Bernstein theorem.
💡 Hint: Consider graphing both sets to visualize the relationships.
Challenge and get performance evaluation