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Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 22, 2012 5:20 AM
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On 2012-02-21, Peter Webb <r.peter.webbbbb@gmail.com> wrote:
> "jbriggs444" <jbriggs444@gmail.com> wrote in message
> http://mathoverflow.net/questions/56633/simple-bijection-between-reals-and-sets-of-natural-numbers
>
> With that in hand, an explicit bijection between the reals
> and the complex numbers would be trivial to construct using
> the digit-interleaving 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 element-wise ones.
Is that trivial enough for you?
--
Tim
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