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    would you call nthrt(x)=x^1/n an equation or identity? i ask because i guess its only true if n is a positive integer greater than 1 and x is a real number, so technically would this be an equation?

    thanks
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    (Original post by 111davey111)
    would you call nthrt(x)=x^1/n an equation or identity? i ask because i guess its only true if n is a positive integer greater than 1 and x is a real number, so technically would this be an equation?

    thanks
    I presume nthrt means n'th root, as such you are defining a function, and that is a "formula", rather than an equation or identity.

    The domain is more restrictive than you've put - what's (-1)^{1/2} for example.
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    (Original post by ghostwalker)
    I presume nthrt means n'th root, as such you are defining a function, and that is a "formula", rather than an equation or identity.

    The domain is more restrictive than you've put - what's (-1)^{1/2} for example.
    I?
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    (Original post by 111davey111)
    I?
    If you're going to start including complex numbers, then what's the cube root of 1? There are 3 of them!

    BUT, this is beside the point as regards your original question.
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    (Original post by ghostwalker)
    If you're going to start including complex numbers, then what's the cube root of 1? There are 3 of them!

    BUT, this is beside the point as regards your original question.
    Yeah true, i don't really get how its a formula.so can you have an identity A=B where the functions have restricted domains. so if you replace n with a 2 is that an identity then?

    Thanks
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    (Original post by 111davey111)
    Yeah true, i don't really get how its a formula.so can you have an identity A=B where the functions have restricted domains. so if you replace n with a 2 is that an identity then?

    Thanks
    If you could tell me what your definition of nthrt(x) is?

    It looks to me that you are defining it there, so you plug in x (and n) and get out the nth root of x, so it's a formula.

    If nthrt(x) is defined in some other way, then you might have an identity, something that is true for all x, within your given domain.
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    (Original post by ghostwalker)
    If you could tell me what your definition of nthrt(x) is?

    It looks to me that you are defining it there, so you plug in x (and n) and get out the nth root of x, so it's a formula.

    If nthrt(x) is defined in some other way, then you might have an identity, something that is true for all x, within your given domain.
    nthrt(x) is meant to be radical notation so its just a different way to write it as opposed to the exponent form on the right.
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    (Original post by 111davey111)
    nthrt(x) is meant to be radical notation so its just a different way to write it as opposed to the exponent form on the right.
    It's a different way of writing the same thing - then it's an identity.

    It's as much of a question as asking whether the relation between \sin^2(x) and [\sin(x)]^2 is an identity or not.
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    (Original post by RDKGames)
    It's a different way of writing the same thing - then it's an identity.

    It's as much of a question as asking whether the relation between \sin^2(x) and [\sin(x)]^2 is an identity or not.
    but the domain changes as you change n doesn't it, so is it only an identity when n is given a number?
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    (Original post by 111davey111)
    but the domain changes as you change n doesn't it, so is it only an identity when n is given a number?
    Yes the domain depends on n but the fact is that this domain will be equivalent for both sides of the relation, and their values will be equivalent as well throughout the domain. This is what an identity is.
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    (Original post by RDKGames)
    Yes the domain depends on n but the fact is that this domain will be equivalent for both sides of the relation, and their values will be equivalent as well throughout the domain. This is what an identity is.
    thanks, so its an identity for n positive integer greater than 1, and it doesn't matter that all x won't give an output due to the restricted domains for even n it only matters for the actual domain of x.
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    (Original post by 111davey111)
    thanks, so its an identity for n positive integer greater than 1, and it doesn't matter that all x won't give an output due to the restricted domains for even n it only matters for the actual domain of x.
    The relation is always an identity on whatever you choose your n to be. If n \in \mathbb{N} then the domain will be x \geq 0 for even n, and x \in \mathbb{R} for odd n.

    No need to be thinking about this too much.
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    (Original post by RDKGames)
    The relation is always an identity on whatever you choose your n to be. If n \in \mathbb{N} then the domain will be x \geq 0 for even n, and x \in \mathbb{R} for odd n.

    No need to be thinking about this too much.
    Thanks
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    (Original post by 111davey111)
    Thanks
    A bit of LaTex would have avoided most of these posts:

    \sqrt[n]{x}\equiv x^{1/n}
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    (Original post by ghostwalker)
    A bit of LaTex would have avoided most of these posts:

    \sqrt[n]{x}\equiv x^{1/n}
    so they would define the same function for all n but 0?

    Thanks
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    (Original post by 111davey111)
    so they would define the same function for all n but 0?

    Thanks
    RDKGames has already answered this: \mathbb{N}=\{1,2,3,...\}
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    (Original post by ghostwalker)
    RDKGames has already answered this: \mathbb{N}=\{1,2,3,...\}
    how come it works for all n on my calculator though? (apart from 0)
    thanks
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    (Original post by 111davey111)
    how come it works for all n on my calculator though? (apart from 0)
    thanks
    I don't understand what you're getting at. In what way does your calculator differ from what's been said on here?
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    (Original post by ghostwalker)
    I don't understand what you're getting at. In what way does your calculator differ from what's been said on here?
    Sorry i didn't understand what you meant by N = (1,2,3) were you saying both sides of the equals only define the same function if n takes these values or will they define the same function for all n but 0
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    (Original post by 111davey111)
    Sorry i didn't understand what you meant by N = (1,2,3) were you saying both sides of the equals only define the same function if n takes these values or will they define the same function for all n but 0
    N={1,2,3...} is just saying what the set of natural numbers is, which RDKGames refered to in his post, i.e. 1,2,3....

    What do you man by "only these values" as compared to "for all n but 0"? How are they different? Are you trying to include fractional and irrational n?
 
 
 
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