??

A Proof That 2 = 1:

let x=y:

X = Y

multiply by x on both sides:

X*X = XY

subtract y*y from both sides:

X*X - Y*Y = XY - 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.

We are not allowed to divide by zero as this is meaningless.

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