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Topic: Bijection Between Complex Numbers and Real Numbers
Replies: 59   Last Post: Feb 24, 2012 7:12 AM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Bijection Between Complex Numbers and Real Numbers
Posted: Feb 19, 2012 3:16 PM

In article
Pubkeybreaker <pubkeybreaker@aol.com> wrote:

> On Feb 19, 12:03 am, Michael Ejercito <mejer...@hotmail.com> 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?
> >
> >  Michael

>
> 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.

That maps the single point r = 0.1000... = 0.0999...
to both the point x = 0.1000..., y = 0.000...
and to the point x = 0.0999... = 0.01 , y = 0.999... = 1, and maps those
two complex points back to a single real point.

And similarly for all the infinitely many reals in [0,1] having dual
representation.
--

Date Subject Author
2/19/12 Michael Ejercito
2/19/12 William Elliot
2/19/12 Virgil
2/19/12 Butch Malahide
2/19/12 Virgil
2/19/12 Shmuel (Seymour J.) Metz
2/20/12 David C. Ullrich
2/20/12 Virgil
2/20/12 David C. Ullrich
2/19/12 Pubkeybreaker
2/20/12 The Perturbator
2/19/12 Pubkeybreaker
2/19/12 Richard Tobin
2/19/12 Michael Ejercito
2/19/12 Kaba
2/19/12 Peter Webb
2/20/12 Kaba
2/20/12 Kaba
2/20/12 Tim Little
2/20/12 Richard Tobin
2/20/12 Peter Webb
2/19/12 Virgil
2/19/12 David R Tribble
2/19/12 Peter Webb
2/20/12 Michael Ejercito
2/20/12 jbriggs444@gmail.com
2/20/12 David Yen
2/20/12 David Yen
2/20/12 David Yen
2/20/12 Peter Webb
2/21/12 jbriggs444@gmail.com
2/21/12 Peter Webb
2/23/12 jbriggs444@gmail.com
2/24/12 Peter Webb
2/24/12 jbriggs444@gmail.com
2/24/12 Peter Webb
2/22/12 Tim Little
2/22/12 Peter Webb
2/20/12 Peter Webb
2/21/12 G. A. Edgar
2/21/12 Peter Webb
2/22/12 Tommy Jensen
2/23/12 Dan Cass
2/23/12 Tommy Jensen
2/21/12 David Yen
2/21/12 David Yen
2/21/12 David Yen
2/21/12 David Yen
2/21/12 David Yen
2/21/12 David Yen
2/22/12 Richard Tobin
2/22/12 David Yen
2/22/12 David Yen
2/22/12 Peter Webb
2/23/12 trj
2/23/12 David Yen
2/20/12 David Yen
2/20/12 David Yen
2/20/12 David Yen
2/20/12 David Yen