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@katemath @sbagley Also nodding to @ProfNoodlearms' reply - it's worth noting that I'm thinking in the context of the real numbers, which I always consider as a subfield of the complex numbers. (But maybe that's unfair to the surreal numbers...)
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@katemath @sbagley @ProfNoodlearms Actually, I take it all back. I've been thinking about the surreals recently, where every number (including reals) is a transfinite sequence of rights and lefts. In that case multiplication by -1 swaps Rs and Ls, which definitely has more of a reflection flavor.