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Page History: Proof that 2=1

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Page Revision: 2009/07/07 08:08


Let
Let a = b

Multiply both sides by a
a2 = ab

Add a2 to both sides
a2 + a2 = a2 + ab

Collecting like terms on both sides
2a2= a2 + ab

Subtracking 2ab from both sides
2a2 - 2ab= a2 + ab - 2ab
= a2 + b2

and
2a2 = 2ab

so

a2 + b2 = 2ab
a2 - 2ab + b2 = 0
(a-b)(a-b) = 0 (Equation 2)

Combining Equations 1 and 2

(a - b)(a + b) = (a - b)(a - b)
a + b = a - b
a + a = a - a
2a = 0a
2 = 0

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