Channel: PBS Infinite Series

Category: Education

Tags: pbsgottleib fregemathematicsinfinitemathsnumbersfundamentalfoundationset theoryrussel's paradoxaxiomsparadoxbetrand russelcrisisfregebottomdedekindlogicismbasiscumulativeaxiom of choicegroundsserieslogicmathaxiom

Description: Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: to.pbs.org/donateinfi What if the foundation that all of mathematics is built upon isn't as firm as we thought it was? Note: The natural numbers sometimes include zero and sometimes don't -- it depends on how you define it. Within logic, zero is always included as a natural number. Correction - The image shown at 8:15 is of Netwon's Principia and not Russell and Whitehead's Principia Mathematica as was intended. Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode How to generate Pseudorandom Numbers? | Infinite Series youtube.com/watch?v=C82JyCmtKWg Mathematics is cumulative -- it builds on itself. That’s part of why you take math courses in a fairly prescribed order. To learn about matrices - big blocks of numbers - and the procedure for multiplying matrices, you need to know about numbers. Matrices are defined in terms of - in other words, constructed from - more fundamental objects: numbers. References:: Probability website mentioned in comments: people.ischool.berkeley.edu/~nick/aaronson-oracle/index.html plato.stanford.edu/entries/philosophy-mathematics plato.stanford.edu/entries/logicism Ernst Snapper :: maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/1980/0025570x.di021111.02p0048m.pdf Philosophy of mathematics (Selected readings) edited by Paul Benacerraf and Hilary Putnam Written and Hosted by Kelsey Houston-Edwards 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!