The Algebra of Natural Number Multisets - Data Structures in Mathematics

Explore the algebra of natural number multisets in this 23-minute mathematics lecture. Delve into deceptively simple yet important notation for dealing with multisets from natural numbers. Learn about augmented addition of multisets with multiples, and discover a list-theoretic description of element multiplicities in given multisets. Consider the potential for extending multiplicities to negative or rational number values, and understand how these concepts contribute to structuring modern algebra using data structures. Gain valuable insights into this foundational topic that bridges pure mathematics and data science.

Introduction
Definition
Notation
New possibilities
Examples