The Awesome Power Of Zero: Redux

Last week I posted a "proof" that 1 = 2 and promised that I would provide the answer at a later date. I am nothing if not true to my word. Now I’m sure that you all know the answer (at least one person does according to the comments – to the top of the class with you, young Luke) but I will go ahead with the answer anyway. So, without further ado, here is the reason that the “proof” is wrong although it looks quite correct.

The Answer

The very first equation in the proof asks us to let a = b. This is the smoke screen behind which the “proof” does its magic trick. All the equations up to and including 4 are correct but the step to equation 5 requires that you divide both sides of equation 4 by (a – b). The smoke screen was set up to blind you to the fact that, since a = b, (a – b) = 0 and you are actually dividing both sides of equation 4 by zero.

Recall from your school days that you must not divide by zero. The “proof” that 1 = 2 is just one example of what happens. It’s bad enough that multiplying by zero turns something into nothing. Dividing by zero unleashes something even more horrible. So don’t do it. Bad things happen. Be afraid. Be very afraid.

 

Coming soon: why the number 1 can be anything but lonely and why the dish ran away with the spoon. Or not.