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What is the value of 0^0?

  1. Jul 13, 2004 #1
    what is the value of 0^0?
  2. jcsd
  3. Jul 13, 2004 #2


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    It's indeterminate, it depends on the way in which you "approach it"
    For example, consider the function f(x) defined on positive numbers:
    Approaching [tex]0^{0}[/tex] by evaluating f at ever closer x's, clearly indicates that:

    Now, consider the function g(x):

    Using g in the limiting procedure, yields [tex]0^{0}=1[/tex]

    That is [tex]0^{0}[/tex] "by itself" is indeterminate
  4. Jul 13, 2004 #3
    so it is a complex number?
  5. Jul 13, 2004 #4
    if x < 0?????????????????????????///
  6. Jul 13, 2004 #5
    You're not allowed to do that? Atleast not with the set of reals?

    As a consequence of one of the multiplication axioms, by definition.

    x^0 = 1
    iff x =/= 0

    there are websites devoted to the number zero and im sure somebody will quote one as usual :P
  7. Jul 13, 2004 #6
  8. Jul 13, 2004 #7
    So if x=0????????????
    What will do?
  9. Jul 13, 2004 #8
    it's not allowed.

    you'll be banished to astrology!

  10. Jul 13, 2004 #9
    So we can't calculate 0^0 like an limite
    So what should we do?
  11. Jul 13, 2004 #10
    why would you want to [tex]0^0[/tex] anyway?
    Last edited: Jul 13, 2004
  12. Jul 13, 2004 #11
    What do u mean Gasso?
  13. Jul 13, 2004 #12
    When I looked last time [tex]0^0[/tex] wasn't defined in maths so it cannot be calculated. It's somewhat similar to [tex]\frac{1}{0}[/tex]. It cannot be calculated, but if some function is approaching it it may converge to some nuber, but it depends on the function.
  14. Jul 13, 2004 #13
    It can calculate but using colex nombers like 1^n
  15. Jul 13, 2004 #14
    Then how much it is?? I'm very curious.
  16. Jul 13, 2004 #15
    What do u mean tomkeus?
  17. Jul 13, 2004 #16
    From my physics viewpoint zero is never zero but a small +/- dx , in this sense 0^0 also involves the non integer root of a negative number
  18. Jul 13, 2004 #17
    I just want to say that [tex]0^0[/tex] isn't real or complex valued like [tex]e^{i\phi}[/tex] or [tex]2^{15}[/tex]. It's indefinite value.
  19. Jul 13, 2004 #18
    No , i think that 0^0 has a value
  20. Jul 13, 2004 #19


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    No, Feynman, not in this universe. It has no specific value. Mathematicians call such objects indeterminate.

    - Warren
  21. Jul 13, 2004 #20

    matt grime

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    Why must it be defined, Feynman? Just because you can write it and think that it looks like it ought ot be a number doesn't mean it is actually such. log(x) can be defined for all real positive x, and if you're prepared to learn some complex analysis for complex non-zero x too, that doesn't mean log(0) is defined.
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