In ch. 2 of Rudin's Principles of Math Analysis, definition 2.18 gives the definition of a closed set: $E$ is closed if every limit point of $E$ is an interior point of $E$. After that, theorem 2.20 and the following corollary clearly state that a finite point set has no limit points. Yet, the immediate example below clearly states that a nonempty finite set is closed. What exactly am I missing because this sounds like a clear contradiction?