Q: Combinatorics (one to one?) Is the following defined as one-to-one?
f: Z → Z, f(n) = ((n+1)/2) + 2
I think it is one-to-one, since for every value of f(n) there is only one value of n. However, when n is 2, f(n) is 3.5, which is not in the realm of Z. Does that mean that the function is not one-to-one?
Since f: Z → Z, are we supposed to only look at the cases where n and f(n) are both in the realm of Z?

A: Let's assume we are dealing with odd integers, (because this maps to $\mathbb{Q}$ if they are even). Suppose not, then there exists $n \neq k$ such that $\frac{n+1}{2}+2=\frac{k+1}{2}+2$. Solving algebraically this implies that $n=k$, a contradiction. Therefore this is one to one.
