Countable Sets
In this video, discuss countable sets, those sets for which all elements can be enumerated into a list. For countably infinite sets, these are sets in one-to-one correspondence with the natural numbers. We prove several examples of countable sets. We prove that countable unions of countable sets are countable, that finite Cartesian products of countable sets are countable, and the set of rational numbers is countable.
This is lecture 35 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 https://drive.google.com/file/d/1a0KG...
This lecture is based upon Section 14.2 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.