>>>>      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?
>
> By using a decimal notation you are equating the set of real numbers
> with the set of integers, thus making the assumption that the set of
> real numbers is countable. Not all real numbers can be represented with
> digits, because digits can only be used to represent a countably infinite
> set, which the set of reals isn't.

I was under the impression that if you allow infinitely long decimal 
expansions then all reals are representable.

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