it doesn't matter whether the number of elements in (1...2006) is even (the answer is yes, because 2006 is an even number). The point is that you have the negative numbers as well. So the number of elements in the set is double the number in (1....2006), so it must be even.
Step by step
that is just the positive integers, and the negative integers (up to 2006).
ie, every positive integer and its negative partner
ie, every element can be paired with another one
so there must be an even number
Edit Posted while plato was typing and not intended to disrespect his answer