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 ]
 David C. Ullrich Posts: 21,553 Registered: 12/6/04
Re: Bijection Between Complex Numbers and Real Numbers?
Posted: Feb 20, 2012 8:06 AM

On Sun, 19 Feb 2012 01:50:02 -0700, Virgil <virgil@ligriv.com> wrote:

>In article
> Butch Malahide <fred.galvin@gmail.com> wrote:
>

>> On Feb 19, 1:25 am, Virgil <vir...@ligriv.com> wrote:
>> > In article <Pine.NEB.4.64.1202182143080.27...@panix3.panix.com>,
>> >  William Elliot <ma...@panix.com> wrote:
>> >

>> > > On Sat, 18 Feb 2012, 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?

>> >
>> > There is certainly no such bijective function which preserves any of the
>> > arithmetical, order or topological properties between the two fields.

>>
>> That seems slightly overstated, in view of the fact that (assuming the
>> axiom of choice) the additive groups are isomorphic.

>
>But one need not assume the axiom of choice.

is false. _Hence_ you cannot _prove_ your assertion, because
a proof of your assertion would then prove "not AC", and that's
impossible.

(Ok, it's impossible if ZF is consistent. When you prove ZF is
inconsistent let us know.)

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