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

Ranch Hand
Posts: 628
Consider the equattion X+X+X...(X TIMES)..
2+2=2^2
3+3+3=3^2

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

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

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

Ulf Dittmer
Rancher
Posts: 42972
73
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
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.