An Interesting Proof

Theorem: for all undirected graph with more than one vertice $G$, there must be at least one pair of vertice $u$ and $v$ ($u, v \in G$) such that $\deg(u) = \deg(v)$.
1. For a connected graph, suppose there are $n$ vertice ($n \gt 1$). According to the property of an undirected graph, for each vertex, the maximum degree is $n-1$. Thus the problem becomes: putting $n$ vertice into $n-1$ boxes numbered from $1$ to $n-1$, and the number on box denotes the degree of vertice in it. It is apparent that there must be at least one box containing two vertice, and thus there must be at least two vertice having the same degree in any connected undirected graph.
$\square$