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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


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    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


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    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


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    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
    2x=x'+x'+x'+... xtimes
    +x+x+x+... x' times
    =1+1+1+... x times
    +x+x+x+... 1 times

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


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    Very interesting actually. I had never thought of that.
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