Peanos Axioms

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http://youtube.com/watch?v=ony0r-UAI7c

This series of videos will develop Mathematics rigorously beginning very near the Foundations. In the first phase I shall start with Peano's Axioms about Natural Numbers and the initial goal will be to develop up to the Real Number System as a complete ordered field. The format of the lectures will be as follows: • 1. Overview • 2. Technical Content (and some History) • 3. Summary of Lecture • 4. Exercise • Solutions to the exercise will be discussed in a subsequent video. • I was inspired by • The Journey of a Thousand Miles starts with a single step Lao Tzu • and have started on a long and arduous journey. • The ultimate goal is to show that most of Mathematics can be developed from Axioms of Zermelo Fraenkel Set Theory. • The first video is on Peano's Axioms and I prove two important properties of the successor functions using the Induction Axiom which will be used extensively in establishing properties of natural numbers. Because of an Introduction to this series this video is about 30 mins. Subsequent videos will be kept under 15 mins. • The videos will be hosted on YouTube on my Channel Old is Gold • / tarananda . • They will also be on Vimeo. • Enjoy! Comments will be welcomed. • ` By studying the masters, not their pupils. • Niels Henrik Abel when asked how he developed his mathematical abilities so rapidly.

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