What is wrong with the proof below that two equals one?

Answer 1

Proof that 2 equals 1.

Given:

a = 1

b = 1

Proof:

a = b

a2 = ab Multiply by a

a2 - b2 = ab - b2 Subtract b2

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

(a + b)(a - b)/(a - b) = b(a - b)/(a - b) Divide by (a - b)

a + b = b

2 = 1

AnswerThe problem arises when you begin dividing by zero, in this case (a-b). It is easy to be distracted by the algebra, (a-b), and miss the fact that since a is equal to b, then (a-b) is equal to zero. As you probably know division by zero isn't allowed in mathematics.