Paradoxes and Infinities

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Paradoxes and Infinities
Math Course
Course CodePDOX
Year Opened2012
Sites OfferedBRI, LAN, SCZ
Previously OfferedATN,EST, HKU, SUN
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Course Description

From the CTY Summer Catalog:

The second sentence is true. The first sentence is false. Are these sentences true or false? How is it that observing an orange pumpkin is seemingly evidence for the claim that all ravens are black? Students in this course explore conundrums like these as they analyze a range of mathematical and philosophical paradoxes.

Students begin by considering Zeno’s paradoxes of space and time, such as The Racecourse in which Achilles continually travels half of the remaining distance and so seemingly can never reach the finish line. To address this class of paradoxes, students are introduced to the concepts of infinite series and limits. Students also explore paradoxes of set theory, self-reference, and truth, such as Russell’s Paradox, which asks who shaves a barber who shaves all and only those who do not shave themselves. Students analyze the Paradox of the Ravens as they study paradoxes of probability and inductive reasoning. Finally, they examine the concept of infinity and its paradoxes and demonstrate that some infinities are bigger than others.

Through their investigations, students acquire skills and concepts that are foundational for higher-level mathematics. Students learn and apply the basics of set theory, logic, and mathematical proof. They leave the course with more nuanced problem-solving skills, an enriched mathematical vocabulary, and an appreciation for and insight into some of the most perplexing questions ever posed.

Class History


PDOX.LAN.23.1 was taught by Blair Seidler and TA'd by Paige. Blair was a fantastic teacher who would often lie to his students for educational purposes. He was very good at making sure students understood everything and also insulting them in the smoothest way possible. Paige was an enigma, whose real name still remains unknown. She was a good math teacher though.

This class was known to switch topics from day to day, or even class to class. It was also mostly taught using the ancient equipment known as "chalkboards". On the first full day of class, the teachers got locked outside of the classroom with all the students inside for half an hour. It was also known for one student referred to as Beck, who was an avid number theorist that tended to do everything in the most complicated way possible. Additionally, all the boys tended to constantly be touching each other in one way or another.


  • "Bob likes homophobes."
  • "You are the y-axis."
  • "I hate it when my emeralds degrue."
  • "Were you asking him a question with your hands?"
  • "Etch this equation into your soul."
  • "I am just a teenage girl, consenting to be drugged."
  • "She's trying to convert me to African!"
  • "Stop singing before I beat you."
  • "Is the devil a furry?"


BRI 16.2: Paradoxes and Infinities B was known for their litness. Everyone was constantly confused and always either playing with a rubrics cube or throwing playing cards at each other. Many of the campers were known for always sleeping during break or class in general. It was also due to this class that the Bleen Team phenomenon occurred. The A team occurred too, originating from PDOX B, consisting of Bonnie Chan, Zyanya Singh, Albert Guo, Elisa "A" Mezhirov, and Abnner Olivares. However, as advised by Abnner, this must be pronounced as ah, since they mustn't be used for copyright. This would be the common thing that Elisa would remember, and always laugh about.


EST 16.1: This class was simply amazing. PDOX at Easton 16.1 was probably the single most functional-dysfunctional class in existence, whether it be because of the wide age range of the people in the class, or the tendency of particular people to regularly check their phones in class, which they were keen to plug in to the wall to charge at the very start of the session. Possibly the most notable events to have occurred in the class were the crucifixion of BEE onto a tree in the green, the uttering of the word 'penetration' during a Foursquare tournament when a mulch chip very aptly so penetrated a ball, the endless printout puzzles we were given to solve, and the frequency with which the class was shown Kurzgesagt and Vsauce videos. Notable members of the class included Theo "Chipmunk" Faugeres, Trrishaant Sarin, Kabir Singh, and Sebastian Reardon. The class unfortunately intersected with a tumultuous period in time, that being the release of Pokémon GO, and the craze seized not only every student within the campus but also some instructors and TAs, among which were those teaching this class. PDOX 16.1. was a great time. It is unfortunate, however, that, after the end of the session, few people in the class kept in touch, and, likely, even fewer still visit the memory of those sunny days in the green or those grey skies seen from Pardee.