Integers amp Reals have different infinite sizes Cantor Diagonlization

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=0HF39OWyl54

Cool Math Episode 1: • Integers Rationals are both infinit... • 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! / 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: / @drtrefor • MATH BOOKS MERCH I LOVE: • ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett

#############################

New on site