Link: https://xkcd.com/2956/
this post was submitted on 09 Jul 2024
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You can do something like this with ℝ[ω] where ω is a complex cube root of unity and the restriction that at least one of the real or ω-part of a+bω must be zero. Edit: Just realised that I didn't specify that a and b should be non-negative reals, otherwise we end up with six lines from 0 not three.
Standard addition breaks immediately, but an addition-like operator can be defined by imagining a train shunting along the restricted lines in the direction of the greater magnitude.
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