Here's the question:
"Suppose that $r_1<r_2<\ldots<r_n$ and $s_1<s_2<\ldots<s_n$ are two increasing sequence of real numbers. Let $\mathfrak{R} = (\mathbb{R};<)$. Write down a formula for an automorphism $\pi: \mathfrak{R} \cong \mathfrak{R}$ such that $\pi(r_i)=s_i$ for each $i=1,\ldots,n$."
I thought I could define $\pi(m)=m$ for $m \not\in \{r_1,\ldots,r_n,s_1,\ldots,s_n\}$, $\pi(r_i)=s_i$ and $\pi(s_i)=r_i$. (Sorry I do not know how to do the multiline equation with a left brace). After thinking over my solution, I think it isn't an automorphism if I have the sequence $1<2<3<4$ and $2<4<6<8$ as $(r_i)$ and $(s_i)$ respectively, because I believe $\pi$ would not be one-one (4 gets send to 2 and 8).
I've been thinking for sometime now but can't find a way around. Any suggestions? Thanks in advance!