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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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David R Tribble

Posts: 3,426
Registered: 7/21/05
Re: Bijection Between Complex Numbers and Real Numbers
Posted: Feb 19, 2012 5:50 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Michael Ejercito 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?

>

Pubkeybreaker wrote:
> 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.


Yep. This is Cantor's mapping of R to R^2, i.e., mapping
the points on a line to the points on a 2D plane. I was
going to suggest exactly the same.

But you still have to handle problematic equivalent decimal
fractions, such as .4999... (from <.4999..., .9999...>) versus
.5000... (from <.5000..., .0000...>).



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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