< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > I couldn't find more informative title! I find difficulties with proofs. So my solution might be weird The problem says "Suppose that x is a fixed non-negative real number such that, for all positive real numbers ε, 0≤ε<x. Show that x=0." My attempt was: Assume 0≤x and x <ε Case 1: 0 <x For evey ε, 0<x and x <ε is false Case 2: 0=x For evey ε, 0=x and x <ε is true My professor was not happy with making cases to proof the statement, and he said this is not a real proof. He suggested starting with the assumption 0 <x and from that I proof 0=x is the wanted fixed non negative real number that satisfies the statement. I am confused. How am I supposed to proof it?