PROOF THAT 1 = 2 !!!!!!

My classmates in Honors Math 3, like anybody else, like to waste time. So  somebody came up with something that took a 1/3 of our class time. It was great. What did he do? He made a math proof, and here it is:

Let a = b

Then a² = b²

Then a² - ab = a² - b²

Factor a(a - b) = (a - b)(a + b)

Cancel a(a - b) = (a - b)(a + b)

Simplify a = a+b

If a = 1, then

       1 = 2

But wait! There's more! You can use this proof so anything equals its double. So 2 = 4, 4 = 8....etc.

Isn't math wonderful?