Does any one know the value of 0^0?

This is a discussion on Does any one know the value of 0^0? within the A Brief History of Cprogramming.com forums, part of the Community Boards category; >>I was following along fine until i hit this post.....thnx magos thats why you need to get yer ass to ...

  1. #16
    Registered User axon's Avatar
    Join Date
    Feb 2003
    Location
    Mt. Prospect, IL
    Posts
    2,572
    >>I was following along fine until i hit this post.....thnx magos

    thats why you need to get yer ass to college buddy....calculus is great, aint it?

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

  2. #17
    RoD
    RoD is offline
    Redundantly Redundant RoD's Avatar
    Join Date
    Sep 2002
    Location
    Missouri
    Posts
    6,331
    i know very (i stress very) little calc, but i always understood 0^0 to be undefined.

  3. #18
    www.entropysink.com
    Join Date
    Feb 2002
    Posts
    605
    Logically it doesn't matter how many times you multiply zero by itself, it's still zero.
    Visit entropysink.com - It's what your PC is made for!

  4. #19
    & the hat of GPL slaying Thantos's Avatar
    Join Date
    Sep 2001
    Posts
    5,681
    Logically it doesn't matter how many times you multiply zero by itself, it's still zero.
    Also logically you can't divide a number by zero. Follow the pattern

    x^2 = (x * x) / 1
    x^1 = x / 1
    x^0 = x / x
    x^-1 = 1 / x
    x^-2 = 1 /(x * x)

    Fill in 0 for x and you find the problem

  5. #20
    Registered User linuxdude's Avatar
    Join Date
    Mar 2003
    Location
    Louisiana
    Posts
    926
    I concur with thantos. I though about it all day at work but you can't divide by zero

  6. #21
    C++ Witch laserlight's Avatar
    Join Date
    Oct 2003
    Location
    Singapore
    Posts
    21,409
    I suppose we get it from:

    x^0 = x^(n-n) = x^n / x^n = 1, but x = 0 => 0 / 0
    where n is some (real, complex?) number.

  7. #22
    Registered User
    Join Date
    Jan 2003
    Posts
    648
    Well see here, conflicting theories:

    x ^ 0 = x / x

    Normally this would equal 1, however:

    if x = 0, x ^ 0 = 0 / 0

    0 / 0 = undefined

    But since any number divided by itself is 1, then it could also be one. But then you can do elementary school reasoning. How many times does 0 go into 0? 0 times.

    So we have three logical answers to 0 ^ 0:

    undefined
    1
    0

    -------------------------------------

    0 ^ 0 = ans

    log[base 0] (ans) = 0

    log ans / log 0 = 0

    log 0 = undefined

    So, even more proof that 0 ^ 0 = undefined.

  8. #23
    Registered User
    Join Date
    Jan 2003
    Posts
    648
    If we say 0 ^ 0 = 1, then there is an identity that denies that.
    log[base b] (b) = 1

    0 ^ 0 = 1
    a ^ b = c
    log[base a] (c) = b
    <substituting>
    log[base 0] (1) = 0

    It does not follow the identity so 0 ^ 0 can't be 1.

    However, another identity states:
    log[base b] (1) = 0

    0 ^ 0 = 1
    a ^ b = c
    log[base a] (c) = b
    <substituting>
    log[base 0] (1) = 0

    Since both identities clash, 0^0 must be undefined. And see the above above post. By definition, a log must not have a base of 0. Therefore you really can't have an exponent with a base of 0. Wierd.

    Anyways I believe: 0 ^ 0 = undefined
    Last edited by Speedy5; 02-21-2004 at 11:09 PM.

  9. #24
    C++ Witch laserlight's Avatar
    Join Date
    Oct 2003
    Location
    Singapore
    Posts
    21,409
    heh, I was about to post about "indeterminate form" when I clicked on the link (which apparently has disappeared)

  10. #25
    Registered User
    Join Date
    Oct 2003
    Posts
    29
    0! = 1

    doesn't it?

  11. #26
    Cat without Hat CornedBee's Avatar
    Join Date
    Apr 2003
    Posts
    8,893
    Yes, but that's merely a definition. 0^0, just as 0/0, are by themselves undefined.
    All the buzzt!
    CornedBee

    "There is not now, nor has there ever been, nor will there ever be, any programming language in which it is the least bit difficult to write bad code."
    - Flon's Law

  12. #27
    Toaster Zach L.'s Avatar
    Join Date
    Aug 2001
    Posts
    2,686
    0! = 1 because it is the same as gamma(1)
    Similarly, 1! = gamma(2), 2! = gamma(3), etc. The gamma function itself is quite nasty though.

    The problem with saying 0^0 is anything is that there are many different ways to get to 0^0, and they don't all have the same limit.

  13. #28
    RoD
    RoD is offline
    Redundantly Redundant RoD's Avatar
    Join Date
    Sep 2002
    Location
    Missouri
    Posts
    6,331
    Originally posted by Zach L.
    The problem with saying 0^0 is anything is that there are many different ways to get to 0^0, and they don't all have the same limit.
    Which is why it is undefined and cannot be anuthing else.

  14. #29
    Rad gcn_zelda's Avatar
    Join Date
    Mar 2003
    Posts
    942
    >>Which is why it is undefined and cannot be anuthing else.

    Not necessarily. 0 raised to itself can be either indeterminant or 1 There are a few discussions of this at PhysicsForums

    And I'm obviously right, because you all know that I'm a inherent genius.

    XD

  15. #30
    Toaster Zach L.'s Avatar
    Join Date
    Aug 2001
    Posts
    2,686
    Originally posted by RoD
    Which is why it is undefined and cannot be anuthing else.
    Precisely.

    It can't be '0 or indeterminate'. It is not well defined (because of the limits)... Not 0... Not anything else. Certainly, there are instances when taking it to be a certain value (e.g. 1 or 0) is convenient, and there is nothing preventing you from treating it as such in those instances, provided that it is understood that the value being used is the limit of a particular function.

Page 2 of 3 FirstFirst 123 LastLast
Popular pages Recent additions subscribe to a feed

Similar Threads

  1. 0 ^ 0 = 1
    By Yarin in forum A Brief History of Cprogramming.com
    Replies: 15
    Last Post: 05-11-2009, 07:21 PM

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21