File APIs for Java Developers
Manipulate DOC, XLS, PPT, PDF and many others from your application.
The moose likes Programming Diversions and the fly likes Puzzle..find out the fallacy...(interesting) Big Moose Saloon
  Search | Java FAQ | Recent Topics | Flagged Topics | Hot Topics | Zero Replies
Register / Login
JavaRanch » Java Forums » Other » Programming Diversions
Bookmark "Puzzle..find out the fallacy...(interesting)" Watch "Puzzle..find out the fallacy...(interesting)" New topic

Puzzle..find out the fallacy...(interesting)

Rambo Prasad
Ranch Hand

Joined: Feb 23, 2006
Posts: 628
Consider the equattion X+X+X...(X TIMES)..

similarly x+x+x+x...(x times)=x^2

Now Differentiate on both side with respect to x
1+1+1...x times = 2x
=>1 =2

What is the mistake here??any idea?
[ March 13, 2006: Message edited by: Rambo Prasad ]

Helping hands are much better than the praying lips
Ulf Dittmer

Joined: Mar 22, 2005
Posts: 42959
The equality is not true (or rather, is not defined) for numbers that are not integers. And since differentiation is defined only for continuous functions -which the one on the LHS is not- it can't be applied here.
Stefan Wagner
Ranch Hand

Joined: Jun 02, 2003
Posts: 1923

Another explanation:
x^2 might be a notation for a function x^2.
But you use it as a value (x^2=x | x=1).
Then you mix both notations, but you may not differentiate a value.
Rambo Prasad
Ranch Hand

Joined: Feb 23, 2006
Posts: 628
Ulf Dittmer

great!correct answer
I agree. Here's the link:
subject: Puzzle..find out the fallacy...(interesting)
jQuery in Action, 3rd edition