??

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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