 By compactness, there is a finite subcover, and since "E""n" are ascending the largest of these is a cover too.Thus we obtain that there is some positive integer "N" such that "E""N" = "X".That is, if "n" > "N" and "x" is a point in "X", then |"f"( "x" ) − "f""n"( "x" )| < ε, as desired.