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 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Dive into learning adventures this summer with our math, science, and contest courses.  Enroll today!
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
Science 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!

4 days
4 days  

Schedule

Mon, Tue, Wed & Thurs
Jul 15 - Jul 18 		7:30 - 9:00
PM ET
Jul 15 - Jul 18
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
Jeffery Yu $145
$145
ENROLL

AoPS Holidays

There are no classes May 25 ‐ 27, July 4, August 30 ‐ September 2, October 31, November 25 ‐ December 1, and December 21, 2024 ‐ January 3, 2025.

Lessons

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

I really enjoyed this course. The class was very fun, with wacky and sometimes unusual problems. It was a nice class with many real world situations that are harder than they may seem. It was certainly challenging but very fun.