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One Equals Two (Posted on 2003-08-22) Difficulty: 3 of 5
Given 'x' not equal to 0, let us consider the follwoing relation:

x + x + x + .... +x (added 'x' times) = x²

Differentiating both sides with respect to x, we get:

1 + 1 + 1 + 1 + .... + 1 ('x' times) = 2x

(Since the derivative of x² with respect to 'x' is 2x).

So we now have:

x = 2x

Cancelling 'x' from both sides, we have:

1 = 2

Now the very obvious question follows:

Where is the flaw ?

  Submitted by Ravi Raja    
Rating: 3.1667 (6 votes)
Solution: (Hide)
Firstly, the above relation holds only for positive integral values of x, and secondly, when we are differentiating with respect to x, the number of times the 1's are occurring is still equal to x, which is not possible, since on differentiation all the x's are changing to 1's.
In other words, saying that you do something 'x' times when you are differentiating with respect to x cannot work.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsGeneral CaseK Sengupta2007-09-26 06:37:27
Some ThoughtsAdditional ConsiderationK Sengupta2007-09-26 06:36:05
SolutionPuzzle SolutionK Sengupta2007-09-26 06:34:59
took a bitJak Dakars2005-03-25 22:04:58
actuallybob9092004-09-21 13:42:52
spelling mistakeBilly Bob2004-04-10 21:29:41
easy explanationjonnyw762003-09-28 20:53:12
Flaw in the ProgramJohnE2003-08-22 12:31:41
SolutionflawsCharlie2003-08-22 08:43:50
SolutionI think I've got it...Your buddy2003-08-22 08:40:55
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