AS/A2 Pure 2 Pure 3

P1 Topic 1: Proof
Fallacy 2
What is wrong with the proof below, which appears to show that one equals negative one?

There are four steps in total. Study each one in turn and see if you can spot the incorrect one. Move the mouse over the line itself and look at the status bar at the bottom to see a brief description of the step.

Summary This fallacy is very difficult to unravel. Writers on mathematics like Martin Gardner and others have discussed it in their books. The problem centres around that the fact that square roots can be positive or negative and the above steps do not make it clear which ones are involved. This page uses WebEQ. To speed up downloading you can install this WebEQ Math Viewer . Click on the Math Viewer icon and you will be taken to the download site.