• Post Reply
  • Bookmark Topic Watch Topic
  • New Topic

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

 
Rambo Prasad
Ranch Hand
Posts: 628
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
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: 42968
73
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
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
Linux Postgres Database Scala
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
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
Posts: 628
  • Mark post as helpful
  • send pies
  • Quote
  • Report post to moderator
Ulf Dittmer

great!correct answer
 
  • Post Reply
  • Bookmark Topic Watch Topic
  • New Topic