TITLE: In any finite graph with at least two vertices, there must be two vertices with the same degree
QUESTION [11 upvotes]: Show that, in any finite graph with at least two vertices, there must be two vertices with the same degree.
HINTS ONLY!

REPLY [4 votes]: Degree of a vertex can range from $1$ to $n-1$ and the number of vertices is $n$. Hence according to the pigeon hole principle at least $2$ vertices will have the same degree.