How to Prove an Element Belongs to a Set
Channel: Andrew Misseldine
Date: 2022-08-18

In this video, we provide a proof pattern of showing whether an object belongs to a given set or not. We also introduce the notion of cardinality of a set. We explore the example of perfect numbers to illustrate that it may be very difficult to determine which elements belong to a set.

This is lecture 2 (part 2/3) 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/1JLbfzqvyB_HrBjOAGvG9I3jw0zyRpzdE/view

This lecture is based upon Sections 1.1, 1.10, and 8.1 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.