Stopped reading here The example I used, was used by our calc professor, on the subjects on proofs (or in this case, INVALID proofs) His whole example went as this: " Example 1.4 We start with: a = 2 We then multiply with A on both sides: a^2 = 2a Subtract 4 from both sides: a^2 - 4 = 2a - 4 apply the Difference of two squares on left side, and factorize out 2 on the right side (a-2)(a+2) = 2(a-2) divide by (a-2) on both sides and get (a+2) =2 but since we started with a = 2 we get 2 + 2 = 2 4 = 2 solution: We've done a couple of formal errors, but the the one that leads to the catastrophic failure is when we divide with (a-2), since (a-2) is (2-2) = 0, which causes Division by Zero. As you see, the whole point was to show division by zero.