I am currently reading Principles of Mathematical Analysis by Walter Rudin. I am a bit confused with theorem 2.41. He is trying to show at one point that if E is a set in ℝk and if every infinite subset of E has a limit point in E, then E is closed and bounded. The proof starts by assuming that E is not bounded. He then says that if this is the case, then E contains points xn such that |xn| > n for each positive integer n. He then constructs a set S that contains all these points xn. Next he says "The set S ... is infinite and clearly has no limit point in ℝk..." I don't see how it is obvious that there is no limit point in ℝk.