The Operation of Caret - Exponentiation via Multisets - Math Foundations

This course develops a novel arithmetic system built from multisets, introducing recursive types, counting functions, addition, multiplication, and a caret operation analogous to exponentiation. It uses concrete examples and connects nested multisets with rooted trees in computer science.

Syllabus

Introduction - historical context of sets
Recursive structures in msets
Review of types
Elements of an mset
General mset notation
Examples of msets and operations
Counting functions on pure msets
Def Z
Def N
Def P
Def M
Operations on msets - addition, multiplication
Caret operation - exponentiation
A slightly more complicated example
Properties of the caret operation
It's all trees