Practice Theorem On Countable Sets (3.5) - Countable and Uncountable Sets
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Theorem on Countable Sets

Practice - Theorem on Countable Sets

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a countable set.

💡 Hint: Think about the types of numbers you can count.

Question 2 Easy

What is a bijection?

💡 Hint: Consider how each element from one set relates to the other.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is a countable set?

A set that is finite and can’t be listed
A set with more than one element only
A set that can be put into one-to-one correspondence with positive integers

💡 Hint: Focus on how we understand counting beyond finite numbers.

Question 2

True or False: The set of real numbers is countable.

True
False

💡 Hint: Recall the characteristics of uncountable sets.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that the set of natural numbers is countable by establishing a bijection with the integers.

💡 Hint: Consider how you can start pairing from 0.

Challenge 2 Hard

Show why the set of rational numbers is countable.

💡 Hint: Think about how to organize and sequence pairs.

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Reference links

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