1. The problem statement, all variables and given/known data Theorem 1.4: Show that every Cauchy sequence is bounded. 2. Relevant equations Theorem 1.2: If [itex]a_n[/itex] is a convergent sequence, then [itex]a_n[/itex] is bounded. Theorem 1.3: [itex]a_n[/itex] is a Cauchy sequence [itex]\iff[/itex] [itex]a_n[/itex] is a convergent sequence. 3. The attempt at a solution By Theorem 1.3, a Cauchy sequence, [itex]a_n[/itex], is a convergent sequence. By Theorem 1.2, a converging sequence must be bounded. Therefore, every Cauchy sequence is bounded. I was just flipping through the textbook that my Analysis class will be using, "Introduction to Analysis" by Edward D. Gaughan, reading through Chapter 1. I noticed this theorem was left to an exercise, but I thought it was a bit too obvious of an answer as these two theorems in the Relevant equations were proven just before it. Is this really as simple as that?