In some part of this forum there was a link to silly math proofs such as 10 = 0, 2 = 1, 3 = 4 and so on. I've slightly modified one of those proofs in order to make it tricky to figure out what is wrong. first of all, A --> B so A and B are almost equal. IIRC, ~ means something like almost equal so I will use it to relate the two. A ~ B then multiply both sides by A A^2 ~ AB then subtract B^2 from both sides A^2 - B^2 ~ AB - B^2 then we factor both sides (A + B) * (A - B) ~ B * (A - B) now divide both sides by (A - B) A + B ~ B since A and B are almost equal, let's half ass simplify B + B ~ B combine like terms 2B ~ B factor out B 2 ~ 1 what the heck? At the step where both sides are divided by A - B, that is NOT a divide by 0 error. Since A and B are not exactly equal, that operation was perfectly legal. So where is the flaw here?