PBS Infinite Series | What Does It Mean to Be a Number? (The Peano Axioms) | Infinite Series @pbsinfiniteseries | Uploaded 6 years ago | Updated 3 hours ago
Viewers like you help make PBS (Thank you đ) . Support your local PBS Member Station here: 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
youtu.be/KZT5hrYOERs
Crisis in the Foundation of Mathematics
youtube.com/watch?v=KTUVdXI2vng
How to Divide by "Zero"
youtube.com/watch?v=uxpowBoPieQ
Beyond the Golden Ratio
youtube.com/watch?v=MIxvZ6jwTuA
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 Euclidâs 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!
Viewers like you help make PBS (Thank you đ) . Support your local PBS Member Station here: 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
youtu.be/KZT5hrYOERs
Crisis in the Foundation of Mathematics
youtube.com/watch?v=KTUVdXI2vng
How to Divide by "Zero"
youtube.com/watch?v=uxpowBoPieQ
Beyond the Golden Ratio
youtube.com/watch?v=MIxvZ6jwTuA
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 Euclidâs 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!
