1. The problem statement, all variables and given/known data Just wondering if I'm understanding the definitions correctly. I honestly feel like an idiot for asking this. 2. Relevant equations A point p is an interior point of E is there is a neighborhood N of p such that N contained in E. A point p is a limit point if the set E if every neighborhood of p contains a point q ≠ p such that q is in element of E. 3. The attempt at a solution It looks like an interior point of E must be contained in E, but a limit point of E is not necessarily contained in E. Am I right?