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Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 19, 2012 9:54 AM
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On Feb 19, 12:03 am, Michael Ejercito <mejer...@hotmail.com> wrote:
> What bijective function exists such that every complex number maps
> to a unique real number, and likewise every real number maps to a
> unique complex number?
>
> Michael
Consider a bijective map from [0,1] to the unit square.
Let r \in [0,1]. Let (x,y) be a point in the unit square.
let r = .a1 a2 a3 .....
Let x = .a1 a3 a5 .....
y = .a2 a4 a6 .....
i.e. take x as being formed from every other digit in the decimal
representation of r. Similarly for y.
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