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God created the real numbers

(www.ethanheilman.com)
136 points Bogdanp | 1 comments | 29 Aug 25 15:31 UTC | HN request time: 0.209s | source
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zamalek ◴[29 Aug 25 20:35 UTC] No.45069094[source]▶
When I truly grokked complex numbers, I felt as though real numbers were a lie - though I would now say that it was a convenient omission. There are many things that are more naturally described using complex numbers - waves (which much of reality boils down to) immediately come to mind. Even if something does align better with real numbers, it's still just x+0i. Maybe I'll change my mind ~when~ if I finally grok quaternions.
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1. znkr ◴[30 Aug 25 09:09 UTC] No.45073151[source]▶
> Even if something does align better with real numbers, it's still just x+0i

Beware, it’s not always useful to work in complex numbers, you sometimes want to do something different for reals and complex numbers. The prime example here is complex analysis. Defining differentiation is based on limits, on the complex plane there are a lot more directions to approach a limit vs just two on the real line. This has some interesting implications. For example, any function differentiable on the complex plane is infinitely differentiable.