The Curious World of Integral Polynumbers - Math Foundations 233

Explore the fascinating realm of integral polynumbers in this 37-minute mathematics lecture. Delve into arithmetic with multisets, incorporating negative numbers and integral arithmetic using particle/anti-particle duality concepts from physics. Discover two ways to expand polynumber arithmetic: introducing integers as coefficients and as exponents. Examine this larger integral polynomial arithmetical world from a purely algebraic perspective, utilizing ideas from physics such as discrete mass distributions and measures. Learn how multiplication corresponds to traditional convolution of measures and uncover a new kind of symmetry crucial for further development. Topics covered include integral polynumbers, IPoly, integers as coefficients, differences between integral polynumbers and functions, IPoly as measures/densities, rational polynumbers (RPoly), reflection symmetry, and symmetric/alternating integral polynumbers.

Introduction
Integral Polynumbers and Ipoly
Integers as coefficients
BIG difference between Integral Polynumbers and functions
In algebra: avoid the "function " concept!
IPoly as measures/ densities
RPoly : Rational Polynumbers
The reflection symmetry
Symmetric /alternating integral polynumbers