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From: hagman on 5 Jun 2010 07:40
On 5 Jun., 05:11, Pollux <frank.ast...(a)gmail.com> wrote:
> I like that bijection. I had started thinking about multiplying a and b in a + bi to get a single real (that would be one half of the bijection, I needed something eld for the other half), but of course, this naive multiplication wouldn't work (z1 = a1 + b1i and z2 = b1 + a1i would map to the same real :-( ). Interleaving is going to work in both directions though. Great!
>
> Thanks for your help!
>
> Pollux

Your next task is to find a bijection that is continuous in one of the
two directions (it can't be i nboth directions) :)

hagman
From: A N Niel on 5 Jun 2010 07:56
In article
<cfd67c23-7633-4968-8e3e-25395b72e6a6(a)x21g2000yqa.googlegroups.com>,
hagman <google(a)von-eitzen.de> wrote:

> On 5 Jun., 05:11, Pollux <frank.ast...(a)gmail.com> wrote:
> > I like that bijection. I had started thinking about multiplying a and b in
> > a + bi to get a single real (that would be one half of the bijection, I
> > needed something eld for the other half), but of course, this naive
> > multiplication wouldn't work (z1 = a1 + b1i and z2 = b1 + a1i would map to
> > the same real :-( ). Interleaving is going to work in both directions
> > though. Great!
> >
> > Thanks for your help!
> >
> > Pollux
>
> Your next task is to find a bijection that is continuous in one of the
> two directions (it can't be i nboth directions) :)
>
> hagman

Why suggest impossible tasks to a beginner?
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