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Welcome to another Mathologer video. Liouvilles number the monster up there consists of infinitely many isolated islands of 1s at the 1! th, 2! th, 3! th, etc. digits with exploding gaps of zeros between them. As I promised you at the end of the last video, todays mission is to show you a nice visual way of seeing that this number is transcendental. Im pretty convinced that as far as transcendence proofs for specific numbers goes, what Ive put together here is as simple and as accessible as it will ever get. Still, if you make it to the end and understand all my arguments I think you can be pretty proud of yourself since not even that many professional mathematicians know any transcendence proofs. And, if you make it to the end, Ive got a special treat for you. Ill show you how you can use Liouvilles number as a template to make a clone of the real numbers within the real numbers. This clone is made up of transcendental numbers like this strange cousin of Pi, but perhaps the cr