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**Function "uniqueness"..**

Ok, pardon the complete lack of terminology here.

I can define a function with one parameter such that no two different inputs give the same output. Example:

f(x) = x + 1

No value of x gives the same result as another value of x.

I believe that it is impossible to define a function which accepts two parameters, yet retains this property of "uniqueness". Am I correct? Is there a name for what I am trying to describe?

I'm pretty sure I am correct, but I have no idea how to prove it.

Lets say I have a function

f(a,b) = k

where k is some sort of calculation.

if k is arithmetic, i can break the uniqueness by doing the calculation outside f, and then feeding 0 as one of the parameters

f(a,b) = k = f(k,0)

if k is geometric I can do the same as above, only pass 1 instead of 0. Outside of these two classes of functions (and the trivial one where a or b is omitted in the calculation of the function) I cant seem to find a good way of proving myself.

Proving this for more and more "classes of calculations" seem futile, I'm not even sure everything can be categorized as neatly as arithmetic and geometric functions can. There might be a better way of going about this?

All feedback is welcome.

k

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