Originally Posted by

**pirateboy** Ah! Sorry! I gave as much information as the book gave! If your curious, the question comes from Charles C. Pinter's "A Book of Abstract Algebra". ...more like "A Book of Abstract Problem Statements"

Anyways, some of the other questions of the section are:

For each integer $\displaystyle n$, define $\displaystyle f_n$ by $\displaystyle f_n(x) = x + n$.

* Prove: For each integer $\displaystyle n, f_n$ is a permutation of $\displaystyle \mathbb{R}$, that is $\displaystyle f_n \in S_{\mathbb{R}}$

* Let $\displaystyle G = \{f_n : n\in \mathbb{Z}\}$ Prove that $\displaystyle G$ is a subgroup of $\displaystyle S_{\mathbb{R}}$

Soo...from context, I'd assume that the domain is $\displaystyle \mathbb{R}$.