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Proof by Smallest Counterexample
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In this video, we introduce the method of Proof by Smallest Counterexample, which comes from the Well-Ordering Principle. We use this to show that the Well-Ordering and Induction Principles are logically equivalent. We use this to prove the Fundamental Theorem of Arithmetic. • This is lecture 21 (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/1EJaH... • This lecture is based upon Sections 6.3, 10.3, 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.
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