
Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 19, 2012 9:54 AM


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.

