# Impossible Sets Episode 9 of Mind-Bending Math: Riddles and Paradoxes

## Related videos

When Measurement Is Impossible
Prove that some sets can't be measured - a result that is crucial to understanding the Banach-Tarski paradox, the strangest theorem in all of mathematics, which is presented in Lecture 23. Start by asking why mathematicians want to measure sets. Then learn how to construct a non-measurable set.
Solving “Impossible” Puzzles
Try your hand at some classic puzzles that have been driving people crazy for centuries involving sliding blocks, jumping pegs, and blinking lights--each of which deals heavily with odd or even numbers. Once you've learned some handy mathematical concepts and tools for solving these puzzles, these fun and exciting games…
Discover the timeless riddles and paradoxes that have confounded the greatest philosophical, mathematical, and scientific minds in history. Stretching your mind to try to solve a puzzle, even when the answer eludes you, can help sharpen your mind and focus - and it's an intellectual thrill!
Everything in This Lecture Is False
Plunge into the world of paradoxes and puzzles with a "strange loop," a self-contradictory problem from which there is no escape. Two examples: the liar's paradox and the barber's paradox. Then "prove" that 1+1=1, and visit the Island of Knights and Knaves, where only the logically minded survive!
Elementary Math Isn't Elementary
Discover why all numbers are interesting and why 0.99999... is nothing less than the number 1. Learn that your intuition about breaking spaghetti noodles is probably wrong. Finally, see how averages - from mileage to the Dow Jones Industrial Average - can be deceptive.