Cardinality of Sets
Channel: Andrew Misseldine
Date: 2022-11-17

In this video, we revisit the topic of cardinality of sets and properly define it using bijective functions. We show that the relation of having the same cardinality is an equivalence. We provide examples of sets that have the same cardinality as the natural numbers and examples of set that have the same cardinality as the real numbers. We show that a set never has the same cardinality as its power set.

This is lecture 34 of the lecture series offered by Dr. Andrew Misseldine for the course Math 3120 - Transition to Advanced Mathematics at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at:  https://drive.google.com/file/d/1ZECiSWd0H0IDdSnczNCTWase4SQ7BwdN/view

This lecture is based upon Section 14.1 of Book of Proof (https://www.people.vcu.edu/~rhammack/BookOfProof/) by Richard Hammack, from the corresponding sections of A Transition to Advanced Mathematics (https://math.byu.edu/~doud/Transition/) by Darrin Doud and Pace P. Nielsen, and from Dr. Misseldine's own notes. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.