Explore a new framework for basic arithmetic and algebra using multisets in this 39-minute lecture. Learn how to define natural numbers, polynumbers, and multinumbers using the concept of multisets, which are unordered collections allowing repetition. Discover inductive definitions for these number systems and understand how arithmetic operations can be generalized within this framework. Examine the closure properties of different number types under addition and multiplication, and investigate the relationship between multisets and computer science. Gain insights into the historical development of this approach and its potential implications for mathematical foundations.