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Home > Math > False Proof: 1 = 2

False Proof: 1 = 2

Suppose a and b are equal and are an arbitrary number

Given: a = b

Multiply both sides by a

a2 = ab

Subtract b2 from both sides

a2 - b2 = ab -  b2

Factor

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

Divide both sides by (a - b)

a + b = b

Substitue b for a, since they're equal (from the given)

b + b = b

Divide both sides by b

1 + 1 = 1

Add

2 = 1

Q.E.D.

Answer (highlight):
a and b are equal, so when you divided both sides by (a - b) you were actually dividing by 0...which is bad. Weird things like this happen.

Come back next week when I show you how to do your taxes in a similar fashion!


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