Practice Countably Infinite Sets (6.1.2) - Module No # 05 - Discrete Mathematics - Vol 2
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Countably Infinite Sets

Practice - Countably Infinite Sets

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a countably infinite set?

💡 Hint: Think of how integers relate to naturals.

Question 2 Easy

Can you list an example of a countably infinite set?

💡 Hint: What can be matched with 1, 2, 3, etc.?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What defines a countably infinite set?

It can't be listed
It has one-to-one correspondence with naturals
It includes irrationals

💡 Hint: Consider counting the elements.

Question 2

True or False: The set of binary strings of infinite length is countable.

True
False

💡 Hint: Remember Cantor's argument.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Using Cantor's argument, prove that the decimal representation of any irrational number is infinite and does not repeat.

💡 Hint: Focus on how equating with rationals fails.

Challenge 2 Hard

Suppose you are asked to list the set of all real numbers. Describe why this is impossible.

💡 Hint: Connect to the earlier discussions about the diagonal.

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