
Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 19, 2012 5:50 PM


Michael Ejercito 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? >
Pubkeybreaker wrote: > 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.
Yep. This is Cantor's mapping of R to R^2, i.e., mapping the points on a line to the points on a 2D plane. I was going to suggest exactly the same.
But you still have to handle problematic equivalent decimal fractions, such as .4999... (from <.4999..., .9999...>) versus .5000... (from <.5000..., .0000...>).

