What Does It Mean to Be a Number The Peano Axioms Infinite Series

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Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi • If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it? • Tweet at us! @pbsinfinite • Facebook: facebook.com/pbsinfinite series • Email us! pbsinfiniteseries [at] gmail [dot] com • Previous Episodes: • Telling Time on a Torus • • Telling Time on a Torus | Infinite Se... • Crisis in the Foundation of Mathematics • • Crisis in the Foundation of Mathemati... • How to Divide by Zero • • How to Divide by Zero | Infinite Se... • Beyond the Golden Ratio • • Beyond the Golden Ratio | Infinite Se... • Are the natural numbers fundamental, or can they be constructed from more basic ingredients? It turns out that you can capture the essence of numberhood in a small set of axioms, analogous to Euclid’s axioms in geometry. They will allow us to build a set N that will behave just like the natural numbers without ever explicitly mentioning numbers or counting or arithmetic as we do so. These axioms were first published in 1889, more or less in their modern form, by Giuseppe Peano, building on and integrating earlier work by Peirce and Dedekind. • 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 (www.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 is supporting us at the Lemma level!

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