This Infinite Math Object Fits in a Surprising Place | SoME4 скачать в хорошем качестве

This Infinite Math Object Fits in a Surprising Place | SoME4

In my video I present from the ground up how to create a continuum sized chain of sets of natural numbers. A surprising object to exist considering that the whole set of natural numbers is countable. I tried to build everything from zero and skip a lot of details and notations so it can be approachable to more people. Starting from what we consider finite and infinite, what are bijections, what are the real numbers and why are they uncountable, then going to the density of rationals and reals. Finally I introduce what is the power set and what is a chain of sets and how it all fits together to create this interesting chain. Despite my attempt at explaining everything and starting off easy, I rush through some parts and after all I think the audience of this video should be at least high-school students with some knowledge of math. Although others could enjoy it as well. Created for the Summer of Math Exposition References: John C. Baez, "This Week's Finds" - https://math.ucr.edu/home/baez/twf.html https://math.ucr.edu/home/baez/twf_la... (week121, p.136) Joel David Hamkins, "The lattice of sets of natural numbers is rich" - https://jdh.hamkins.org/the-lattice-o... References Vodeos: Vsauce, "Banach-Tarski Paradox" -    • The Banach–Tarski Paradox   Veritasium, "The Man Who Almost Broke Math (And Himself...) - Axiom of Choice" -    • The Most Controversial Idea In Math   minutephysics, "How to Count Infinity" -    • How to Count Infinity   #SoME4 #SoME