Channel: PBS Infinite Series

Category: Education

Tags: setpbs spacetimenumberphilemathematicsmathsnumbersset theorycomputerphilepeanomeanvon neumann ordinalmathpeano axiomstheoryaxiom

Description: Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: to.pbs.org/donateinfi In the physical world, many seemingly basic things turn out to be built from even more basic things. Molecules are made of atoms, atoms are made of protons, neutrons, and electrons. So what are numbers made of? Check out the previous episode to find out What It Means to be a Number youtube.com/watch?v=3gBoP8jZ1Is And to see Gabe's solution to the Torus Clock Challenge check out: bit.ly/pbs_clock_challenge Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode: What Does it Mean to Be A Number? youtube.com/watch?v=3gBoP8jZ1Is Torus Clock Challenge: youtube.com/watch?v=KZT5hrYOERs How to Divide by "Zero" youtube.com/watch?v=uxpowBoPieQ&t=3s Blog post about the Peano axioms and construction of natural numbers by Robert Low: robjlow.blogspot.co.uk/2018/01/whats-number-1-naturally.html Recommended by a viewer for connections to formulation of numbers in computer science: softwarefoundations.cis.upenn.edu Any set N and function S that meet these conditions will *behave* , respectively, like the natural numbers and the operation "next" or "successor". You can even define operations that fully mimic run-of-the-mill addition and multiplication in terms of any suitable S, regardless of the details of how S works . In this sense, the Peano axioms distill numberhood down to its bare essentials. Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (kornhaberbrown.com) Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon. Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level! And thanks to Mauricio Pacheco who are supporting us at the Lemma level!