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Re: Bijection Between Complex Numbers and Real Numbers
Posted:
Feb 19, 2012 10:03 AM
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In article <cb39da8d-c390-4a10-a159-2fdaa5c7e22a@l14g2000vbe.googlegroups.com>,
Pubkeybreaker <pubkeybreaker@aol.com> 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.
Though this has the usual problem with multiple representations. For
example, both 0.1 and 0.00909090... map to (0.1, 0).
-- Richard
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