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?

3 comments:

  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.

    ReplyDelete
  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.

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

    I'm glad you found it interesting steph.

    ReplyDelete

Leave your answer or, if you want to post a question of your own, send me an e-mail. Look in the about section to find my e-mail address. If it's new, I'll post it soon.

Please don't leave spam or 'Awesome blog, come visit mine' messages. I'll delete them soon after.

Enter your Email and join hundreds of others who get their Question of the Day sent right to their mailbox


Preview | Powered by FeedBlitz


The Lamplight Manor Puzz 3-D
Are you looking for a particular puzzle, riddle, question, etc? Or do you want to find the answer today rather than wait till tomorrow!
Google