Channel: PBS Infinite Series

Category: Education

Tags: pbsmultiversemathematicsinfinitenumberspoissonjacobiconcatenationseriesloopcommutativitypropertygerstenhaberassociativemultiplicationmathassociahedronmultiplyassociativitypropertiescommutative

Description: Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: to.pbs.org/donateinfi What happens if you multiply things that aren’t numbers? And what happens if that multiplication is not associative? Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode The Heat Equation + Special Announcement | Infinite Series youtube.com/watch?v=NHucpzbD600 Multiplication of numbers is an associative property and we can make sense of “multiplication” between things that aren’t numbers but that’s not considered as associativity. And since we’re talking about associativity, you might wonder about that other property of real numbers: You know: when multiplying two numbers, swapping their order doesn’t change the answer. This property is called commutativity. But keep in mind: it’s a very special property to have! Not everything in life is commutative. For example, getting dressed in the morning... putting on your socks and then your shoes is NOT the same as first putting on your shoes and then your socks. Link to Resources: The Fundamental Group: ‘Loop concatenation’ math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Landau.pdf Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (kornhaberbrown.com) Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level! And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!