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Math Help - To the power of zero; zero exponent

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    To the power of zero; zero exponent

    I searched for a discussion of the rules governing exponents of zero but didn't find anything so I thought I'd start a thread on it.

    We have learned that any number raised to the power of zero is equal to 1. Why is that so? Also, does this apply to zero, that is, zero raised to the power of zero?
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    To answer this question is beating a dead horse. But it is summer.
    We know the rules of exponents: \frac{{x^5 }}{{x^3 }} = x^{5 - 3}  = x^2 .
    Therefore we would have to allow 1 = \frac{{x^5 }}{{x^5 }} = x^{5 - 5}  = x^0.
    But we never allow division by zero!
    Therefore, it can be argued that 0^0 is not defined.
    But if you look at the first link, you will see that this is very old argument.
    The great Euler argued that 0^0 = 1.

    Math Forum: Ask Dr. Math FAQ: Zero to Zero Power
    Math Forum: Ask Dr. Math FAQ: N to Zero Power
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    Forum Admin topsquark's Avatar
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    I have heard of conventions stating that 0^0 = 1 and 0^0 = 0. But these are just conventions used in specific cases to generalize a result. As Plato says, this is not a defined operation so it is undefined.

    -Dan
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    Quote Originally Posted by Cifrocco View Post
    We have learned that any number raised to the power of zero is equal to 1. Why is that so? Also, does this apply to zero, that is, zero raised to the power of zero?
    (e^x) (e^0)= e^x+0 = e^x and hence e^0 = 1 for all e in the set R (Real numbers)

    What is 0^0?? I asked my Maths Professor that question 15 years ago; His answer was: God knows
    Last edited by Math's-only-a-game; May 27th 2009 at 09:56 AM.
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    Quote Originally Posted by Math's-only-a-game View Post
    (e^x) (e^0)= e^x+0 = e^x and hence e^0 = 1 for all e in the set R (Real numbers)
    For all? Did you then divide by zero?
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    Quote Originally Posted by Plato View Post
    For all? Did you then divide by zero?
    Are you trying to say: If for all e in R then e = 0 ==> e^x = 0^0 = ??

    Well spotted; I should have said "for all {R - 0}" i.e for all Real numbers except 0.

    My Apologies

    Btw I have sent you a private message; have you received it?? I was asking how do you type/copy/paste the maths text. I have try it with Mathcad, Math type 6 and Word with no success.

    I would highly appreciate any help from anyone.
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    Quote Originally Posted by Math's-only-a-game View Post
    [COLOR=navy]Btw I have sent you a private message; have you received it?? I was asking how do you type/copy/paste the maths text. I have try it with Mathcad, Math type 6 and Word with no success.
    Using MathType you can produce LaTeX code. Choose LaTeX tranlators found under Preferences. By coping an expression you get this code \[\frac{{\partial x}}{{\partial y}}\] which you then edit to [tex]\frac{{\partial x}}{{\partial y}}[/tex] to produce <br />
\frac{{\partial x}}{{\partial y}}.
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    Quote Originally Posted by Plato View Post
    Using MathType you can produce LaTeX code. Choose LaTeX tranlators found under Preferences. By coping an expression you get this code \[\frac{{\partial x}}{{\partial y}}\] which you then edit to [tex]\frac{{\partial x}}{{\partial y}}[/tex] to produce <br />
\frac{{\partial x}}{{\partial y}}.
    Thanks for the info. However I can't get the preferences options activated possibly because I have the free version. In other words to use the preferences options I would have to buy the software.

    Thanks anyway. Much obliged
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    Quote Originally Posted by Math's-only-a-game View Post
    I can't get the preferences options activated possibly because I have the free version. In other words to use the preferences options I would have to buy the software.
    Even with the free version.,TeXAid, it works. Go to perferences, pulldown that tab the first option is Translators. Ckick translators an new window appears. Click translate to other languages(text). In the window below that select TeX--LaTex2.09 and later. Uncheck any boxes below that.
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    Quote Originally Posted by Plato View Post
    Even with the free version.,TeXAid, it works. Go to perferences, pulldown that tab the first option is Translators. Ckick translators an new window appears. Click translate to other languages(text). In the window below that select TeX--LaTex2.09 and later. Uncheck any boxes below that.
    That's exactly what I've tried but for some reason none of the options under preferences can be activated. Maybe the software is corrupted. I should try to re-download the software but I don't know if they will allow me to do so, for I used my free trial.

    Thanks for your concern

    Zack
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  11. #11
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    Download TeXAide. It is free. But does not work with Word.
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    Quote Originally Posted by Plato View Post
    Download TeXAide. It is free. But does not work with Word.
    {\rm x}^{\rm n} {\rm + y}^{\rm n} \ne {\rm z}^{\rm n} {\rm }\forall {\rm n > 2}

    Yes, it worked!!!

    I tried to leave space between the {\rm z}^{\rm n} the "for all" and n but no success.

    No matter; it's still much better than the rubbish I was posting before.

    Thanks Plato; you are a good man .
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  13. #13
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    Quote Originally Posted by Plato View Post
    We know the rules of exponents: \frac{{x^5 }}{{x^3 }} = x^{5 - 3}  = x^2 .
    Therefore we would have to allow 1 = \frac{{x^5 }}{{x^5 }} = x^{5 - 5}  = x^0.
    But we never allow division by zero!
    Stupid question... Why does the argument not apply to all powers of zero? ( 0^n=0^{n+1}/0^1=0/0)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sleepingcat View Post
    Stupid question... Why does the argument not apply to all powers of zero? ( 0^n=0^{n+1}/0^1=0/0)
    dividing by zero is invalid, always. 0^n would be defined otherwise. for instance, if n is an integer, we may define it as 0 times itself n times, and so on
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  15. #15
    MHF Contributor Mathstud28's Avatar
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    I would like to add, that although straight up 0^0 is undefined

    Things of the form \lim_{x\to{c}}f(x)^{g(x)} where f(c)=0 and g(c)=0 can yield theoretically and value one chooses
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