More arithmetic with negative msets | Math Foundations 232 | N J Wildberger

Let's illustrate this new box arithmetic using anti msets to define negative numbers, with some more explicit examples. This involves using integers not just for coefficients of polynomumbers / polynumbers, but also to crucially extend the possibilities for exponents to negative numbers. This introduces a vital symmetry into the world of algebra with polynumbers that is almost entirely missing from usual algebra courses: where essentially Laurent polynomials appear not in a calculus / analysis context, but as pure objects of analysis.

This will have major consequences for our understanding of algebra going forward.

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Video Contents:
00:00 More Arithmetic with negative msets
04:26 Anti-objects!
07:14 Negative msets
09:09 Examples of integer arithmetic
13:06 Examples of integer polynumber arithmetic
19:42 Multiplicative arithmetic with integer polynumbers
28:55 Integral (Laurent) polynumbers
32:57 Arithmetic with integral polynumbers

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