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What does 0^0 equal?

  1. Jul 15, 2010 #1
    1. The problem statement, all variables and given/known data

    It's a word problem, but I just need to simplify 0^0.

    2. Relevant equations

    n/a

    3. The attempt at a solution

    0^n = 0.
    n^0 = 1.




    I'm just going through a calculus book on my own this summer. It's not even a calculus question, but I've never come across this before. Which is it? 0 or 1? Why?
     
  2. jcsd
  3. Jul 15, 2010 #2
    Re: 0^0

    I believe it's 0 (or not even defined, such as in poles of a polynom), because from what I can remember n^0 = 1 is by definition only true for those n that are different from 0.
     
    Last edited: Jul 15, 2010
  4. Jul 15, 2010 #3
    Re: 0^0

    0^0 is undefined.
     
  5. Jul 15, 2010 #4
    Re: 0^0

    From Wolfram Mathworld http://mathworld.wolfram.com/ExponentLaws.html

    The definition 0^0=1 is sometimes used to simplify formulas, but it should be kept in mind that this equality is a definition and not a fundamental mathematical truth (Knuth 1992; Knuth 1997, p. 56).
     
  6. Jul 15, 2010 #5
    Re: 0^0

    Okay, thanks guys. Wolfram is awesome!
     
  7. Jul 15, 2010 #6

    LCKurtz

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    Re: 0^0

    Consider the binomial expansion:

    [tex] 1 = 1^2=(x+(1-x))^2 =\binom 2 0 x^0(1-x)^2+\binom 2 1 x^1(1-x) + \binom 2 2 x^2(1-x)^0[/tex]

    This doesn't work for x = 0 or 1 unless you define 00 = 1. That is an example of why it is usually defined as 1. Also why 0! = 1 in the same example.
     
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