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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.
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