
Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 19, 2012 10:03 AM


In article <cb39da8dc3904a10a1592fdaa5c7e22a@l14g2000vbe.googlegroups.com>, Pubkeybreaker <pubkeybreaker@aol.com> 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.
Though this has the usual problem with multiple representations. For example, both 0.1 and 0.00909090... map to (0.1, 0).
 Richard

