Subject: calculus Name: sporky Who is asking: Student Level: Secondary Question: Why does the proof for 1=2 not work? x = 1 x2 = 1 x = x2 1 = 2x (derivitive) 1 = 2(1) 1 = 2 ???  please tell me where the false logic is. Hi, Draw a picture showing y = x and y= x2. On the picture, you will see TWO things: at x=1, the two graphs cross.  when they cross, they do NOT have the same tangent line and therefore they do not have the same derivative. So the "=" in line three is an "=" of points, not of functions or graphs. You do not take the derivative of a point - but of a graph. It would now be your choice as to WHICH of lines 3 or 4 you wanted to say had the flaw in logic. The way to test the logic in such a string of equations is to substitute, in each line, and SEE when the statements SWITCH from true to false. Good logic always takes a true statement to a true statement. Anything that takes a true statement to a false statement is bad logic! Line 3 is written as if you can substitute any value of x. However, it is only true if x= 0 or 1. Walter Go to Math Central