(A, B) is an interval in the real line. If I take the middle point (B-A)/2, and then take the middle point of each of the two subintervals of (A,B), and then take the middle point of each of the four subintervals of (A, B) and I go on this indefinitely, can I be sure that sooner or later I will touch any point of (A, B)? (I know that there are infintely many irrationals in (A, B) but I am carrying this process "to the limit"). Maybe dumb question but I need your support. Thanks.