How to prove that in an arbitrary graph the number of vertices with odd degree is even

Question

I know that degree of a vertex of an (undirected) graph is the number of edges incident to the vertex. I need to prove that in an arbitrary graph the number of vertices with odd degree is even. How to formally prove it?

Answer 1

The sum of degrees of all vertices is even. Thus the number of odd-degree vertices must be even, since otherwise the first sum is odd (even-degree vertices do not affect the parity of the first sum).

Answer 2

I proved this many hard ways. Years later I found this. This is the best way!