Partially Ordered Sets
In this video, we discuss the notion of a partial order, which is a relation which is reflexive, antisymmetric, and transitive. A set equipped with a partial order is a partially ordered set (or a poset). We present some examples. We discuss how to prove that a relation is a partial order. We also introduce Hasse diagrams in order to better visualize posts.
This is lecture 25 (part 1/3) 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/1dHaP...
This lecture is based upon Sections 11.2, 7.2, and 5.3 of Book of Proof (https://www.people.vcu.edu/~rhammack/...) 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.