Practice Cardinality Of Infinite Sets (3.2) - Countable and Uncountable Sets
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Cardinality of Infinite Sets

Practice - Cardinality of Infinite Sets

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the cardinality of the set {A, B, C}?

💡 Hint: Count the elements in the set.

Question 2 Easy

Is the set of all even numbers countable or uncountable?

💡 Hint: Can you list the even numbers in a sequence?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which symbol denotes the cardinality of countably infinite sets?

ℵ₀
C

💡 Hint: Think about what symbol we learned for countably infinite sets.

Question 2

True or False: The set of all integers is uncountable.

True
False

💡 Hint: Remember how we can list integers in a sequence.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider the set of all rational numbers. Determine if it is countably infinite and provide a proof.

💡 Hint: Try constructing a diagonal argument to illustrate the listing of rationals.

Challenge 2 Hard

What can you infer about the power set of a countably infinite set? Is it countable or uncountable?

💡 Hint: Reflect on how many subsets a set has and consider Cantor's argument.

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