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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

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 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