On 13/07/2013 05:47 PM, Warp wrote:
> Orchid Win7 v1<voi### [at] devnull>  wrote:
>>> 2) If yes, that means there has to be a 1-to-1 mapping between those
>>> points. Give a function that expresses such a mapping.
>
>> Given the 2D coordinates of a point on the unit square, you can
>> interleave their decimal digits, which always yields a unique point on
>> the unit line. For example,
>
>>     0.3425
>>     0.2183 ->  0. 32 41 28 53
>
> That doesn't work because it's not a one-to-one mapping. Ie. the mapping
> is not unambiguous.

That would imply that two distinct 2D points exist which map to the same 
1D point. Can you provide such a counter-example?

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