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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: 42965
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
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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)
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