An Elegant Pairing Function [pdf]
szudzik.com|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 ?
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
to[a0 a1 a2 a3...] [b0 b1 b2 b3...]
I am not sure that is a computable function for infinite-length bit sequences, though. Maybe none of those mapping functions are?[a0 b0 a1 b1 a2 b2 a3 b3...]Ah yes, I was thinking |N x N| = |N|. So is there a pairing function f: NxN -> N which can be used as compression?