
Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 22, 2012 5:20 AM


On 20120221, Peter Webb <r.peter.webbbbb@gmail.com> wrote: > "jbriggs444" <jbriggs444@gmail.com> wrote in message > http://mathoverflow.net/questions/56633/simplebijectionbetweenrealsandsetsofnaturalnumbers > > With that in hand, an explicit bijection between the reals > and the complex numbers would be trivial to construct using > the digitinterleaving approach. > __________________________________________ > If its trivial, produce the bijection.
Let the function defined in the linked article be denoted f:R>P(N). Then the bijection is g:C>R given by g(a+bi) = f^1((2f(a)+1) u (2f(b))).
The arithmetic operations on the sets of naturals are defined to be the obvious elementwise ones.
Is that trivial enough for you?
 Tim

