Monday, October 24, 2005

I've proven 1 = 2

Or have I?

Here is the proof...

(1) X = Y Given
(2) X2 = XY Multiply both sides by X
(3) X2 - Y2 = XY - Y2 Subtract Y2 from both sides
(4) (X+Y)(X-Y) = Y(X-Y) Factor both sides
(5) (X+Y) = Y Cancel out common factors
(6) Y+Y = Y Substitute in from line (1)
(7) 2Y = Y Collect the Y's
(8) 2 = 1 Divide both sides by Y
Can you spot the error?


  1. Since X = Y,

    (X+Y)(X-Y) = Y(X-Y) --- (1)
    (X+Y)(0) = Y(0)
    0 = 0
    You cannot cancel the common factors of (X-Y) from (1)

    So the error lies in step 4 to 5.

    Interesting post. Very intriguing.

  2. The problem is in step 4.
    You multiply both sides by (x-y). As x = y, you are multiplying by zero.
    Multiplying by zero always yields magical results.

  3. That's right. You can't divide by zero! That's always a mistake.

    I'm glad you found it interesting steph.


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