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

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Tim Little

Posts: 1,793
Registered: 2/7/09
Re: Bijection Between Complex Numbers and Real Numbers
Posted: Feb 22, 2012 5:20 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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


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

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