Art of Problem Solving
AoPS Online AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy AoPS Academy
Small live classes for advanced math
and language arts learners in grades 1-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

The time is now - Spring classes are filling up!
How Classes Work
Course Catalog
Recommendations
Subject Courses
Before Prealgebra Ready for Prealgebra After Prealgebra Some Algebra 1 After Algebra 1 After Geometry After Algebra 2 After Precalculus Beyond Calculus
Contest Preparation
MATHCOUNTS/AMC 8 AMC 10 AMC 12 AIME USAMO
Computer Programming
Little or No Experience Some Experience Extensive Experience
Physics Courses
Little or No Experience Some Experience Extensive Experience
Prospective Students & Parents
Math Jams
Need Help?

Need help finding the right class? Have a question about how classes work?

Click here to Ask AoPS!

Paradoxes and Infinity

In this class we'll explore several popular paradoxes and attempt to wrap our brains around the world of infinity. For example, we'll discover a hotel that's never full: somehow, this hotel can always add another guest, or two, or three. We'll also run into paradoxes about goats, haystacks, pop-quizzes and more. If you're interested in mind-bending ideas and theories and have a background in basic algebra, this class is for you!

6 hours
6 hours  

Schedule

Sat & Sun
Nov 16 - Nov 17 		4:00 - 7:00
PM ET  –
Nov 16 - Nov 17
4:00 - 7:00 PM Eastern
3:00 - 6:00 PM Central
2:00 - 5:00 PM Mountain
1:00 - 4:00 PM Pacific
Click here to see more time zones
Kathryn Lesh $150
$150
CLOSED

AoPS Holidays

There are no classes November 25 ‐ December 1, December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, and October 31, 2025.

Topics

1 Paradoxes in Philosophy
2 Paradoxes in Mathematics
3 Hilbert's Grand Hotel and Infinite Cardinals
4 Zeno's Paradox of Dichotomy

I really enjoyed the material covered in this class. I not only learned how to do a variety of problems,but also I discovered quicker methods of solving problems I already knew how to do. I also was thrilled by the difficulty on these problems; in most other non-AOPS courses I get problems that I can do in 2 seconds. Another thing I found fantastic is that the course instructors answered all of my problems,questions,and concerns.