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A Multiset Approach to Arithmetic - Math Foundations

Insights into Mathematics via YouTube

Overview

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This course introduces a multiset-based framework for arithmetic and algebra. It defines natural numbers, polynumbers, and multinumbers as nested multisets and develops their addition and multiplication.

Syllabus

Introduction and history of multiset development
A multiset mset is an unordered collection allowing repetitions
A natural number NAT is an mset of zeroes
A polynumber is an mset of natural numbers
A multinumber is an mset of polynumbers
Addition of msets
NAT is closed under addition and commutative, associative
Multinumbers are also closed under addition
Multiplication of msets of msets
Each "type domain" is closed under addition and multiplication
The meaning of "poly"
Distinction of mset and list
Mathematics as a topic in computer science

Taught by

Insights into Mathematics

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