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0^0=0 method

  1. Oct 23, 2005 #1
    a friend [no longer a user of the forum]showed me this and i felt i should as well show this to you all
    let x^x=x
    x^[1/x]=x
    x^[1/x]-x=0
    x[x^(1/x-1)-1]=x
    so x is 0 and 1.
    which evntually gives 0^0 as 0
    in sloving with anither method,he also got -1 as x.
    how true is the topic 0^0=0.
    he explained that if you have nothing and you raise it to nothing you eventually get nothing.
     
  2. jcsd
  3. Oct 23, 2005 #2
    How did you get from the first step to the second ?
     
  4. Oct 23, 2005 #3
    If you have x = 0, you get 1/0 which is invalid.
    I also fail to see how you got from the first to the second equation.
     
  5. Oct 23, 2005 #4
    I don't actually see how the first equation is valid , never mind the second one.

    Could somebody please explain ?
     
  6. Oct 23, 2005 #5
    It's valid because he wants to solve x^x = x, for x.
     
  7. Oct 23, 2005 #6
    mathelord, this is all pretty trivial. What is it that's confusing you? If you "have nothing and you raise it to nothing", then you don't have anything to exponentiate! You don't "eventually" get nothing, it was always nothing.
     
    Last edited: Oct 23, 2005
  8. Oct 23, 2005 #7
    Factoring x from 0 and getting x is some pretty nontrivial algebra. :rofl:
     
  9. Oct 23, 2005 #8
    I don't see how he was "factoring x from 0 ". Anyway, It wouldn't be hard to construct a proof that shows that the equation [tex]x^{x}=x[/tex] is only valid for 0 and 1. So......
    [tex]0^{0}=0[/tex]
    [tex]1^{1}=1[/tex]

    Fiddle-dee-do
     
  10. Oct 23, 2005 #9

    Zurtex

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    Well:

    [tex]\lim_{x \rightarrow 0} x^x = 1[/tex]

    [tex]\lim_{x \rightarrow 0} 0^x = 0[/tex]

    Some times 00 = 1 is defined as for usefulness, but in general its not determined.
     
  11. Oct 23, 2005 #10
    Look at his fourth step.
    It would be impossible. 00 is an indeterminate form. See here and here.
     
  12. Oct 23, 2005 #11
    x^0=1 any number raised to zeor power equals 1. x*x*x*x...*x zeor ammount of times equals 1 because 1 is the null value in multiplication. a number times himself zero times is equal to 1.
    0^x=0 zero raised to any power equals zero. 0*0*0*0*0*...0=0 because of multiplication property. no matter how many zeors you have...you still have zero.

    0^0=? Well...is it 1 becasue it is raised to zeor parts? or is it 0 becasue the 0 is raised to a power? Can't be both, but it can be none. answer: undefined.
     
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