Let A be the set of real numbers x such that 0<x<=1. For every x element of A, let E sub x be the set of real numbers y such that 0<y<x. Then for x in A the intersection of all Esubx is empty. I do not understand that the intersection is empty. I see that my index set is infinite and that as x approaches zero the magnitude of the sets Esubx become infinitely small so that the intersection is not abtainable but does that mean it is non-exisitant? Rudin suggests I note that for every y>0, y not in Esubx if x<y. Hence y not in the insection of all Esubx. I have a problem understanding this suggestion. My index set is bounded above and and not bounded below. It seems to me that y could be greater than or equal to x but not just greater than x. Vastly confused?!??!