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Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 19, 2012 5:50 PM
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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...>).
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