1. The problem statement, all variables and given/known data Show if K contained in R is compact, then supK and inf K both exist and are elements of K. 2. Relevant equations 3. The attempt at a solution Ok we proved a theorem stating that if K is compact that means it is bounded and closed. So if K is bounded that means that for every element k in K there exists an M in R so that, |k|<M which is equiv to: -M<k<M meaning for all k in K k>-M and k<M and therefore K is bounded above AND below. According to the axiom of completeness, that means that the supK and the infK exists. Alright, this is where I get stuck, I know that the supK and infK are the limit points of K, and since we know that K is closed, they would be contained in K, but I don't know how to show that supK and infK are the limit points. Any help would be great!