The Division Algorithm for Polynumbers - Arithmetic + Geometry Math Foundations | N J Wildberger

Explore the division algorithm for polynumbers in this 45-minute lecture from the MathFoundations series. Learn about natural numbers, integers, fractions, and rational numbers before delving into their polynomial counterparts. Discover two approaches to dividing integral polynumbers: one starting with lower order terms and another with higher order terms. Examine positive polynumbers, integral polynumbers, and rational polynumbers, and work through exercises to reinforce your understanding. Gain insights into the logical foundations of mathematics and explore the similarities between polynomial division and long division of ordinary numbers.

Intro to the division algorithm
Positive polynumbers
Extension and re-evaluation of polynumbers
Integral polynumbers
Rational polynumbers
Exercise
Division algorithm
Division algorithms starting with highest powers
Division using polynumber form