The Solution To: And Two Shall Become One

Here was the original problem:

I am going to show you a mathematical proof that proves 2 = 1.

Let a = b Then a * a = a * b; that is a2 = ab a2 – b2 = ab – b2 (a – b)(a + b) = b(a – b) a + b = b b + b = b 2b = b 2 = 1

Multiply both sides by a Subtract b2 from both sides Factor both sides (left side uses the difference of squares rule) Divide both sides by (a – b) Replace a with b since a = b Combine like terms Divide both sides by b Voila! 2 = 1

Now we all know that 2 does not equal one. So tell me what mathematical "no no" I committed. I'm not trying to trick you. I actually did break a mathematical rule. You just have to figure out what it is!

Here is the solution:

When I divided both sides by (a - b), I was actually dividing by zero, which isn't allowed.  Since a = b,   a - b = 0.  Dividing by 0 is undefined (at least in ordinary arithmetic, which is the kind we all use) and is a "no no" so to speak.

:)

Sincerely,
The Math Freak