What IS a Number? As Explained by a Mathematician

Ever wondered how numbers are actually defined? In this video, you’ll learn the most common way it’s done by mathematicians. I really want to make more of these, so please consider supporting me by buying me a coffee using the link below! Buy me a coffee: Channel: Website: My website may be a good place to start if you’re confused... 00:00 - Intro 02:19 - Motivation 04:12 - Physical Units: An Analogy 08:26 - First Attempt 10:39 - The Perils of Intuition 12:40 - Definition in Principle 15:38 - Sets and Russell’s Paradox 23:44 - Rules of Sets 31:46 - Constructing the Numbers 38:25 - Cake 38:29 - Closing Remarks *Galileo’s Paradox: In his final book, which bears the catchy title, “...,“ Galileo discusses the size of the set of natural numbers versus that of the set of square numbers (not e