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A Proof That 2 = 1:
let X = Y:
X = Y
multiply by X on both sides:
X.X = X.Y
subtract Y.Y from both sides:
X.X - Y.Y = X.Y - Y.Y
factorise:
(X + Y)(X - Y) = Y(X - Y)
divide by (X - Y) on both sides:
(X + Y) = Y
replace X with Y:
Y + Y = Y
factorise:
2Y = Y
divide by Y on both sides:
2 = 1
Where lies the flaw in the logic?
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Answer
On line 4 we are dividing both sides by (X - Y).
But we know that X = Y, so X - Y = 0.
Dividing by zero is undefined, so we are not allowed to do this.
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