Hello,

I would like to define a function from Z --> ZxZ that is both onto and one to one. I think it is going to have to be a piecewise function, but I am totally lost on how to get started. What I do know is that the function can be represented graphically by a spiral where the inputs and outputs look something like this:

f(0) = (0,0)

f(1) = (1,0)

f(2) = (1,1)

f(3) = (0,1)

f(4) = (-1,1)

f(5) = (-1,0)

f(6) = (-1,-1)

f(7) = (0,-1)... so on

I know this is only for positive Z, and this is part of the reason I am stuck. I am also not sure how to represent this info as a function. Any help would be appreciated. This is bugging the crap out of me. Thank you.