Polynumbers are extensions of the positive numbers 0,1,2,3... and have an arithmetic which is the same as that of polynomials. In fact polynumbers present us with a more logical and fundamental approach to polynomial arithmetic.This video presents some basic definitions, such as the degree of a polynumber, and then explains addition and multiplication of polynumbers. The latter is not much different from the way you multiply ordinary numbers!This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics.
Does mathematics make logical sense? No, it does not. Foundational issues have been finessed by modern mathematicians, and this series aims to turn things around. And it will have interesting things to say also about mathematics education---especially at the primary and high school level. The plan is to start right from the beginning, and to define all the really important concepts of basic mathematics without any waffling or appeals to authority. Roughly we discuss first arithmetic, then geometry, then algebra, then analysis, then set theory. This course is aimed for a general audience, interested in mathematics, or willing to learn.