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I don't fully understand what you meant. Either I misunderstood it or there is a problem with your explanation. You can measure distance between complex number
by lokedhs 5y ago
I don't fully understand what you meant. Either I misunderstood it or there is a problem with your explanation.
You can measure distance between complex numbers. But the distances between three numbers has a non-transitive relationship which is what prevents ordering.
Was that what you meant, or is there some more fundamental relation between not having an order and the idea of distances?
- joe__f 5y agoReal numbers have a unique canonical ordering (up to isomorphism). So given x and y real, it is always true that either x < y, x = y or x > y. Complex numbers don't have a unique ordering. So for for example take 1+i and 5-2i. Which is bigger? There are many possible orderings that you can define on the complex numbers. The fact that ordering them is not unique means that any such order is a choice rather than a property of the numbers themselves. You're thinking about measuring distances in the complex plane which is absolutely fine, and also has a canonical definition. I was referring to the fact that it's not intrinsically meaningful to say that 'London is (5000+250i)km from New York'
- galaxyLogic 5y agoComplex numbers are strange and wonderous because of the rules about their interactions including how they always seem to be a sum of an imaginary and real part.