## 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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