Proof that in a graph of $2$ or more vertrex, there's at least $2$ of them that have the same degree

Question

That's what I what to prove let $G$ be an undirected graph such it has $2$ or more vertex, there's at least $2$ vertex that have the same degree.

I'm almost certain that, supposing that it's possible to have a undirected graph such every of it's vertex degree is different, and trying to construct this graph, I'll get a contradiction. But I don't know how to formalize this.

Any help?

Answer 1

Hint 1: If there are $n$ vertices, what is the largest possible degree? What are the possible degrees, if they are all different?

Hint 2: It is possible to have a vertex of maximal degree, and another one of degree 0?