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The Big Step from Polynumbers to Multinumbers - Math Foundations - N J Wildberger

Insights into Mathematics via YouTube

Overview

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This course develops arithmetic from nested multisets, moving from polynumbers to multinumbers. It introduces notation and operations for building an algebraic framework over multiple variables.

Syllabus

introduction
Pure msets are formed with only [ ]
Basic principle: pure msets can be described completely, unambiguously
Operations on pure msets
Addition: dump the contents of added msets into a new mset
Multiplication: add distributed combinations of the contents of msets
Modifying polynumber terminology / notation
α0 ≡ [ 1 ]
α1 ≡ [ α0 ]
α1 is the first multinumber that is not a polynumber
Basic arithmetic with polynumbers
But there are more multinumbers!
More arithmetic examples
Algebra in variables - α0, α1, α2, ... - extend Poly to Bi Poly
creating a tight framework for Algebra
Next: on a strange vessel on uncharted waters?

Taught by

Insights into Mathematics

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