And Two Shall Become One

Here is the problem of the week:

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!

Good luck.  Answer will be posted Sunday!

Sincerely,
The Math Freak