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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
Sep 13 - Sep 14 		4:00 - 7:00
PM ET  –
Sep 13 - Sep 14
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
Ray Garner $155
$155
CLOSED
Sat & Sun
Apr 18 - Apr 19 		4:00 - 7:00
PM ET  –
Apr 18 - Apr 19
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
Carlos Bovell $155
$155
ENROLL

AoPS Holidays

There are no classes December 20 ‐ January 2, May 23 ‐ 25, July 3 ‐ 5, September 5 ‐ 7, October 31, and November 23 ‐ 29 2026.

Topics

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

Great course. As a senior in high school I decided to take this course as I had never been exposed to math that required problem solving in my education, let alone discrete math. With this class I went from almost no discrete math knowledge (and commensurately poor problem solving skills) to a place where I will be taking the 400-level combinatorics sequence at my University in a few months and have had concurrent improvement in my problem solving ability.