Recall the one-to-one and onto mapping of the set of natural numbers to the set of integers. We used this mapping to show that the integers were countably infinite. Find a function, f(n) that gives the nth integer of the given mapping below. You may find it useful to know that the floor(x) of a number is the largest integer that is less than or equal to x. You may use the floor in your final answer.
Examples: floor(4.3) = 4
floor(10.789) = 10
floor(8) = 8
floor(-2.6) = -3
Mapping:
N Z
1 0
2 1
3 -1
4 2
5 -2
6 3
7 -3
... ...