Cantor's Diagonal Argument: The rationals and reals have different sizes?!?!?

Video Description

Cool Math Episode 1: https://www.youtube.com/watch?v=WQWkG9cQ8NQ In the first episode we saw that the integers and rationals (numbers like 3/5) have the same "size" - that is there is a bijective function so that you can line up the integers and rationals even though they are infinite sets and even though the rationals has elements like 3/5 that aren't in the integers. In this episode, we now compare the integers and the REAL numbers. Using Cantor's Diagonalization Argument, we attempt to list all the real numbers - that is, find a bijection between the integers and the reals. However, we then construct a new real number not on the list, which shows that the reals and the integers can NOT have the same size. ******************************************************* Follow me on twitter! https://twitter.com/TreforBazett ******************************************************* Now it's your turn: 1) Summarize the big idea of this video in your own words 2) Write down anything you are unsure about to think about later 3) What questions for the future do you have? Where are we going with this content? 4) Can you come up with your own sample test problem on this material? Solve it! Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK. Hope you enjoyed! BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett