Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

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

 Messages: [ Previous | Next ]
 Peter Webb Posts: 122 Registered: 11/21/11
Re: Bijection Between Complex Numbers and Real Numbers
Posted: Feb 20, 2012 9:34 PM

"Richard Tobin" <richard@cogsci.ed.ac.uk> wrote in message
news:jhtdqe\$163e\$1@matchbox.inf.ed.ac.uk...
> In article
> Michael Ejercito <mejercit@hotmail.com> wrote:
>

>>> Though this has the usual problem with multiple representations. For
>>> example, both 0.1 and 0.00909090... map to (0.1, 0).

>
>> That is correct. This would imply that each complex number maps
>>onto MULTIPLE real numbers, and certainly the reals can not have a
>>GREATER cardinality than the complexes.

>
> Given a surjection both ways, the dual Schroder Bernstein theorem
> shows that there is a bijection.

But doesn't provide an obvious bijection. And this is using a comparatively
advanced result to prove that a solution to a simple problem exists.

> This however relies on the axiom
> of choice.
>

No. Cantor Bernstein Schroder does not require AoC. It is constructive.

> If we take the interleaved digits as a base-11 number we have an injection
> both ways, and standard Schroder Bernstein gives us a bijection.
>
> -- Richard

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