Row and column polynumbers | Arithmetic and Geometry Math Foundations 65 | N J Wildberger

Описание: This video introduces a two-dimensional aspect to arithmetic by considering both polynumbers written as columns and as rows, and then putting those two ideas together to define bipolynumbers, whose coefficients form a rectangle. The associated polynomials are written in two variables, alpha and beta, which now have a distinguished meaning as special polynumbers.

This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics.

Video Content:
00:00 Intro to row and column polynumbers
4:07 Row polynumbers
9:08 Arithmetic of column/row polynumbers
11:12 Example of division
16:56 Simplified arithmetic
23:54 Two-dimensional arithmetic
29:01 Multiplication of Bi polynumbers
32:01 Definition of a Bi polynumber
35:31 Labelling of coefficients
42:04 Standard alpha beta form
47:01 Exercises

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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated.

***********************
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses are being developed at openlearning.com. The first one, already underway, is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at Patreon,   / njwildberger   . Your support would be much appreciated.

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