Proving π is irrational using high school level calculus

I did make one big typo/mistake in the video: at 3:40 I claimed that f(x) is a polynomial with integer coefficients. I meant to write n!f(x) is a polynomial with integer coefficients. Commenter ffggddss also pointed out some other typos/smaller mistakes in the video which I have pinned to the top. As it's impossible to simply edit the video on YouTube, I have created a blog post that goes over the algebra in more detail, and it should be free of these mistakes: http://mindyourdecisions.com/blog/201... For the original source, the video is based on Ivan Niven's "A Simple Proof Pi is Irrational". The paper is available on Project Euclid: http://projecteuclid.org/DPubS/Reposi... If you like my videos, you can support me at Patreon:   / mindyourdecisions   Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: http://mindyourdecisions.com/blog/ Twitter:   / preshtalwalkar   Facebook:   / 168446714965   Google+: https://plus.google.com/1083366085665... Pinterest:   / preshtalwalkar   Tumblr:   / preshtalwalkar   Instagram:   / preshtalwalkar   Patreon:   / mindyourdecisions   Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) https://www.amazon.com/gp/product/150... "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/152... "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/151... "Math Puzzles Volume 2" is a sequel book with more great problems. https://www.amazon.com/gp/product/151... "Math Puzzles Volume 3" is the third in the series. https://www.amazon.com/gp/product/151... "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) https://www.amazon.com/gp/product/151... "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150... "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/150...