Mathematical puzzle

[altivo]

This thing popped up as a fortune cookie on Linux this morning. It took me a while to figure out where the error was. Let's see who can find it first.

Proof that 2 equals 1:

x = y	[Given]
x2 = xy	[Multiply both sides by x]
x2 - y2 = xy - y2	[Subtract y2 from both sides]
(x + y)(x - y) = y(x - y)	[Factor]
(x + y) = y	[Cancel out (x - y) term]
2y = y	[Substitute x for y, by original equation]
2 = 1	[Divide both sides by y]

I'll supply the answer after folks take a crack at it. It isn't as hard as it looks, and someone may get it right away, so replies are screened for now. It was credited to Omni Magazine.

Answer:
I declare quaxo the first to put his paw right on the heart of the error, though you were all on the right track. If X = Y, then (X - Y) = 0. And the fourth step ("Cancel out (X - Y) term") is actually a divide by zero error. Up to that point, everything was perfectly kosher, even though some of it was nonsensical. After that, nothing is right.

Comments

[kint.livejournal.com]

If X = Y then X - Y = 0, therefore you cannot divide both sides of the equation by (X - Y) to cancel them out

[altivo.livejournal.com]

You got it. :) Divide by zero and you can make anything happen.