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I wonder if this further demonstrates the reality of the complex domain and the anachronism of the real number line? In that, numbers are “circularly” or ultima
by achillesheels 6y ago
I wonder if this further demonstrates the reality of the complex domain and the anachronism of the real number line? In that, numbers are “circularly” or ultimately geometrically countable and not sequentially?
- ogogmad 6y agoThe complex numbers are also uncountable.
- fractionalhare 6y agoIt does not demonstrate that, no. Complex numbers are no more "real" than real numbers are. They are uncountable, as another commenter said. In general they share many properties with real numbers because the sets C and R^2 are isomorphic and isometric with respect to each other.
- achillesheels 6y agoI was ignorant of the mathematically rigorous definition of countability, thanks.
- mike00632 6y agoThink of the complex numbers chiefly as all the solutions to polynomials with coefficients that are real. The number "i" is the solution to the polynomial 0 = x^2 + 1. We choose to use a letter instead of a number simply because the numbers are already being used, similar to how hexadecimal uses letters.
- achillesheels 6y agoI like “imagining” them as geometrical because of the logical necessity of motion in the complex plane when processing their mathematical operations.