Two equals One

Pseudo-proof of that 2 = 1

Watch closely: I will prove that 2 = 1. Your job is to show why such a logical proof could possibly be wrong. It isn't sufficient to point out that the answer is ridiculous.

Let:

a =

a² =

a² - b² =

(a - b)(a + b) =

a + b =

2b =

2 =

ab - b²

b(a - b)

definition

multiply both sides by a

subtract b²

factor

cancel like terms

since a = b

divide by b

Q.E.D.

It looks logical. But it isn't. Can you spot the flaw?