I want to prove this claim using contradiction:
Let $G$ be a simple graph with $n$ vertices. Prove by contradiction that $G$ has two vertices having the same degree (Consider the vertex of smallest degree and vertex of largest degree).
I think I know where to start. The vertex of the largest degree is $n-1$ in this graph and the smallest is 1. How can I use contradiction to prove the statement above? I studied the proof of this using pigeonhole but I wanna use contradiction this time.