

An Elegant Pairing Function [pdf] - codeismightier
http://szudzik.com/ElegantPairing.pdf

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sorokod
|R x R| = |R| so the existence of such functions is guaranteed but it is nice
to see that some are just a method call away. Does anyone know what pairing
function on non negative integers is the most efficient in the number of bits
it requires ?

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Someone
This PDF only handles mapping N x N to N and vice versa, though.

For R x R, I would mix the bits of the two numbers

    
    
      [a0 a1 a2 a3...]
      [b0 b1 b2 b3...]
    

to

    
    
      [a0 b0 a1 b1 a2 b2 a3 b3...]
    

I am not sure that is a computable function for infinite-length bit sequences,
though. Maybe none of those mapping functions are?

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sorokod
Ah yes, I was thinking |N x N| = |N|. So is there a pairing function f: NxN ->
N which can be used as compression?

