Orbits were defined before Exercise 11. Leta, b A and a S A - Show that if O a. and O b. have

Orbits were defined before Exercise 11. Leta, b ∈ A and a ∈ S_A- Show that if O_a.σ and O_b.σ have an element in common then O_a.σ and O_b.σ.

Orbits defined

Let A be a set and let σ ∈ S_A· For a fixed a ∈ A, the set 

O_a.σ- = {σⁿ(a) |n ∈ Z}

is the orbit of a under σ.