Originally Posted by

**Ryaη** I'm given: Let A be a set and let $\displaystyle \sigma \in S_A$. For a fixed $\displaystyle a \in A$, the set

$\displaystyle O_{a,\sigma} = ${$\displaystyle \sigma^n (a)|n \in Z$}

is the orbit of a under $\displaystyle \sigma$.

I have to prove:

Let $\displaystyle a,b \in A$ and $\displaystyle \sigma \in S_A$. Show that if $\displaystyle O_{a,\sigma}$ and $\displaystyle O_{b,\sigma}$ have an element in common, then $\displaystyle O_{a,\sigma} = O_{b,\sigma}$.

The statement makes sense, I just have no idea what to do when it comes to proving it.