4. Let ECR be a set of real numbers and {n}n be a sequence of real numbers (not necessarily contained in E). Suppose that lim xnx, nX where x is an interior point of E. Show that there is N = N such that an E for all n > N (the sequence may start out outside of E, but if it converges to an interior point of E, then eventually - after a certain threshold - the sequence has to live inside E).