Practice Proof By Contradiction (6.1.6) - Module No # 05 - Discrete Mathematics - Vol 2
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Proof by Contradiction

Practice - Proof by Contradiction

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a countable set?

💡 Hint: Think about how you could list its elements.

Question 2 Easy

Give an example of an uncountable set.

💡 Hint: Recall Cantor's diagonalization argument.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Cantor's diagonal argument demonstrate?

That certain sets are countable
That certain sets are uncountable
That all sets are finite

💡 Hint: Focus on the distinction between listing and counting.

Question 2

Is the set of all finite binary strings countable?

True
False

💡 Hint: Consider how you can list finite strings.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

If you had a list of all binary strings ranging up to a certain length, how might Cantor's argument show that there are still strings missing?

💡 Hint: Consider how flipping bits reveals unseen elements.

Challenge 2 Hard

Why can’t we use Cantor’s diagonalization for rational numbers?

💡 Hint: Reflect on the definitions of rational and irrational.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.