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Puzzle ZIHG 



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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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