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    i was wondering how something to the power of zero is one, ive never understood why but just know that it is.
    e.g 34 to the power of zero = 1
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    (Original post by johnface)
    i was wondering how something to the power of zero is one, ive never understood why but just know that it is.
    e.g 34 to the power of zero = 1
    I think the following pattern might help

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    Hmm, I'm not actually sure... I've always thought "it just is"!
    I suppose if I have a number, and I times it by itself 0 times... you get 1? Maybe it's the same as dividing it by itself?
    Hmm.......
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    This looks quite helpful:
    http://mathforum.org/dr.math/faq/faq...to.0power.html
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    I've always thought of this in terms of division:

    Obviously x/x = 1

    Division in terms of the difference in the indicies: 1 - 1 = 0 and so x0 = 1
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    (Original post by johnface)
    i was wondering how something to the power of zero is one, ive never understood why but just know that it is.
    e.g 34 to the power of zero = 1
    \frac{x^y}{x^y}\equiv \ x^{0} \equiv \ 1
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    (Original post by rupertj)
    \frac{x^y}{x^y}\equiv \ x^{0} \equiv \ 1
    that's the worst jibberish ive ever seen
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    (Original post by johnface)
    that's the worst jibberish ive ever seen
    How, exactly?

    \frac{x^y}{x^y}=1, of course, because it's something divided by itself. But \frac{x^y}{x^y}=x^0 as well, since it's equal to x^{y-y}.
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    (Original post by johnface)
    that's the worst jibberish ive ever seen
    Seriously? Anything over itself is always 1, so x^0 is 1. Makes perfect sense?
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    (Original post by johnface)
    that's the worst jibberish ive ever seen
    I'm afraid he's right...
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    (Original post by Tyrrell9)
    Seriously? Anything over itself is always 1, so x^0 is 1. Makes perfect sense?
    Thank you. :yep:
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    (Original post by Tyrrell9)
    Seriously? Anything over itself is always 1, so x^0 is 1. Makes perfect sense?
    Not true.

    Nought divided by nought does not equal one.
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    (Original post by steve2005)
    Not true.

    Nought divided by nought does not equal one.
    Nought isn't 'anything', it's nothing.

    Does that work?
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    If you only work with integer powers than it's probably best just to accept this as a definition, so that rules like a^(x+y)=(a^x)(a^y) work. Otherwise it's a consequence of the definition of the exponential function.
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    (Original post by Sh4w)
    Nought isn't 'anything', it's nothing.

    Does that work?
    But nothing still goes into nothing infinitely many times, thus being undefined.
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    If you think about the theory of subtracting powers when dividing, then it's fairly self explanatory.
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    Sorry to hijack this thread, but what I really don't understand is why \displaystyle \lim_{x \to \infty} 1^x is an indeterminate form, it just goes totally against the definition of 1^n = 1 \  \forall n \in \mathbb{R^+}. Can anyone explain this to me?
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    (Original post by Emc2)
    Sorry to hijack this thread, but what I really don't understand is why \displaystyle \lim_{x \to \infty} 1^x is an indeterminate form, it just goes totally against the definition of 1^n = 1 \  \forall n \in \mathbb{R^+}. Can anyone explain this to me?
    It's not. It's 1.
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    (Original post by generalebriety)
    It's not. It's 1.
    Wikipedia begs to differ. And so does my high school calculus textbook.

    EDIT: sorry if that came across as arrogant, it's just frustration for not being able to get my head around it really
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    (Original post by Emc2)
    Wikipedia begs to differ. And so does my high school calculus textbook.
    I don't see the expression you posted on that Wikipedia page anywhere. Can you type out precisely what your textbook says and/or point me to the line you're talking about on that page?
 
 
 
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