Practice - Listing of Set S
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Practice Questions
Test your understanding with targeted questions
What is the definition of cardinality?
💡 Hint: Think about how we can count elements in a group.
Give an example of an injective mapping.
💡 Hint: Consider functions that don’t pair different elements together.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What theorem states that two sets have the same cardinality when there are injective mappings both ways?
💡 Hint: Recall the theorem focused on injective mappings.
True or False: There exists a countably infinite subset in every infinite set.
💡 Hint: Think about the properties of sets with infinite particles.
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Challenge Problems
Push your limits with advanced challenges
Using the mapping concept, prove that both (0, 1) and (0, 1] have the same cardinality systematically.
💡 Hint: Consider visual aids for the mappings.
Construct two uncountable sets with finite intersection. Explore their properties.
💡 Hint: Use boundaries of sets for example constructions.
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Reference links
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