1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A strange fact as well as big doubt

  1. Nov 29, 2008 #1
    We know x^2 = x*x*x*x... x times
    If we differentiate both sides with respect to x, we have
    2x=1+1+1+... x times
    i.e. 2x=x
    i.e 1=2
    How is it possible or am i making a mistake?

    Please helpp!!!!
     
  2. jcsd
  3. Nov 29, 2008 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Erm, well to start with x2 = x*x
     
  4. Nov 29, 2008 #3
    I'm assuming you meant x+x+x+x... x times.

    The problem with trying to take the derivative of that with respect to x is first, the number of terms changes as well as each term itself, and second, you can't really write it like that if x is not a nonnegative integer.
     
  5. Nov 29, 2008 #4

    nicksauce

    User Avatar
    Science Advisor
    Homework Helper

    And even if x is a nonnegative integer, your function, f(x) = x+x+x... (x times), is only defined at the nonnegative integers, so your function f(x) isn't continuous anywhere, so it can't be differentiated.
     
  6. Nov 29, 2008 #5

    lurflurf

    User Avatar
    Homework Helper

    Your way of handling addition and multiplication is confused as you have not prperly defined what x times means. That aside the problem with your differentiation is that for a derivative to be correct all x in the function must be allowed to vary, you hold your x times fixed.
    x^2=x+x+x+... xtimes
    differentiate
    2x=x'+x'+x'+... xtimes
    +x+x+x+... x' times
    =1+1+1+... x times
    +x+x+x+... 1 times
    =x+x=2x

    So the problems were holding the x in "x times" fixed and not properly defining what "x times means.
     
  7. Nov 29, 2008 #6

    nicksauce

    User Avatar
    Science Advisor
    Homework Helper

    Very interesting actually. I had never thought of that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A strange fact as well as big doubt
  1. Strange function (Replies: 2)

  2. Strange integral (Replies: 4)

  3. Strange Symbol (Replies: 1)

Loading...