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kgilpin
on July 21, 2018
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The Octonion Math That Could Underpin Physics
As far as I know, addition is something you define (an axiom) in order to construct the real (or other) numbers.
https://sites.math.washington.edu/~hart/m524/realprop.pdf
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Search:
https://sites.math.washington.edu/~hart/m524/realprop.pdf