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

Explore the concept of multinumbers in this 35-minute mathematics lecture. Delve into a new arithmetic system based on multisets, expanding from polynumbers to multinumbers. Learn about pure msets, their operations, and modified polynumber notation. Discover the first multinumber that is not a polynumber and practice basic arithmetic with polynumbers. Investigate more complex multinumbers and their arithmetic examples. Extend polynomial algebra to bi-polynomial algebra using variables α0, α1, α2, and create a tight framework for algebra. This lecture provides a foundation for understanding a more flexible and expansive approach to arithmetic, with potential applications in computer science.

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
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