Как можно сломать теорию множеств — за 900 секунд

Subscribe to the RTVI Telegram channel: https://t.me/rtvimain If you don't know what set theory is, mathematical PhD candidate Denis Fufaev will explain who invented it and why, what the "cardinality" of a set is, how one infinite set can be infinite, what the Cantor diagonal is, and whether set theory can be broken. Ready to learn everything about set theory in 15 minutes? Set the timer! Subscribe to @NauchDok and like us! RTVI News — all the main events 24/7:    / myrtvi   00:00 "900 Seconds." Set Theory 00:28 How does the example of a mathematician checking into a full hotel relate to set theory? 01:27 What is a set? 02:13 Who invented the set and why? 02:51 What types of sets are there? 03:24 What is the "cardinality" of a set? 05:24 How can one infinite set be more infinite than another? 06:24 What is the Cantor diagonal? 08:51 Why is the set of all subsets of an infinite set more "infinite" than the set itself? 10:08 What is the paradoxical nature of the set of all sets? 10:52 How did one example break set theory? 12:01 Have mathematicians found a way out of the crisis caused by Russell's paradox? 12:53 What is the axiom of choice? 14:33 Kurt Gödel hammered the final nail into the mathematical coffin. Why?