Hi guys, I have to teach inequality proofs and am looking for an opinion on something. Lets say I have to prove that a2+b2≥2ab. (a very simple example, but I just want to demonstrate the logic behind the proof that I am questioning) Now the correct response would be to start with the inequality (a - b)2≥0, then progress to: a2+b2-2ab≥0 ∴ a2+b2≥2ab. What many students do, as it is generally much easier, is to start with the required result and work backwards: i.e. a2+b2≥2ab a2+b2-2ab≥0 ∴ (a - b)2≥0, which is true, ∴ the initial result must also be true. Can anyone provide an example where starting with the result and working toward a true statement will not work? My colleagues would generally discourage this approach but it would be much more convincing to students if I could show them a situation where it won't work. Thanks for the help guys!