Is the Null Set a Subset of All Sets? (Axiomatic Set Theory)
2,403 views · Published 23 October 2018 · 3:57 · Indexed 26 September 2026
Channel: Carneades.org · 2018 · Education
This video contains a proof of the claim that the null set is a subset of all sets and classes. This series covers the basics of set theory and higher order logic. In this month we are looking at the properties of sets and classes, including transitive sets, swelled sets, supercomplete sets, ordinary sets, proper subsets, null sets, empty sets, universal sets, and void sets. We are also looking at the first four axioms of a basic universe, following Neumann Berneays Gödel (NBG) set theory. In the next month we will look at relationships between sets. Sponsors: João Costa Neto, Dakota Jones, Thorin Isaiah Malmgren, Prince Otchere, Mike Samuel, Daniel Helland, Mohammad Azmi Banibaker, Dennis Sexton, kdkdk, Yu Saburi, Mauricino Andrade, Diéssica, Will Roberts, Greg Gauthier, Christian Bay, Joao Sa, Richard Seaton, Edward Jacobson, isenshi, and √2. Thanks for your support! Donate on Patreon: https://www.patreon.com/Carneades Buy stuff with Zazzle: http://www.zazzle.com/carneades Follow us on Twitter: @CarneadesCyrene https://twitter.com/CarneadesCyrene Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy, Set Theory and the Continuum Problem by Smullyan and Fitting, Set Theory The Structure of Arithmetic by Hamilton and Landin, and more! (#SetTheory)
