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    (Original post by the bear)
    solution = {roots}

    {solutions} = {}
    In this context, it is standard to say 'a solution' to mean 'a value of  x that makes the equation true.'
    i.e. {solutions of  1 + \sqrt{x^2 + 4} - x - \sqrt{2x + 1} = 0 } = {roots of 1 + \sqrt{x^2 + 4} - x - \sqrt{2x + 1}}

    Using the plain English definition of 'solution', sure, there is only one solution to the problem - the set written above.
    (Even then, what you've written is incorrect: {solutions} = {{roots}}.)
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    (Original post by studentro)
    In this context, it is standard to say 'a solution' to mean 'a value of  x that makes the equation true.'
    i.e. {solutions of  1 + \sqrt{x^2 + 4} - x - \sqrt{2x + 1} = 0 } = {roots of 1 + \sqrt{x^2 + 4} - x - \sqrt{2x + 1}}

    Using the plain English definition of 'solution', sure, there is only one solution to the problem - the set written above.
    (Even then, what you've written is incorrect: {solutions} = {{roots}}.)
    it is incorrect to refer to more than one solution to an equation.
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    (Original post by the bear)
    it is incorrect to refer to more than one solution to an equation.
    While what you're suggesting does seem like a more sensible way of using the word, it is standard practice to use it the way I've described. Asking google/a teacher/a professor will confirm this.
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    (Original post by studentro)
    While what you're suggesting does seem like a more sensible way of using the word, it is standard practice to use it the way I've described. Asking google/a teacher/a professor will confirm this.
    it's just that in math we use words precisely ?
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    (Original post by the bear)
    it's just that in math we use words precisely ?
    As I've said, ask google/a teacher/a professor. 'Precisely' does not mean 'perfectly in line with the everyday English definition'.
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    (Original post by studentro)
    As I've said, ask google/a teacher/a professor. 'Precisely' does not mean 'perfectly in line with the everyday English definition'.
    this is the math forum, not the "everyday English forum" :toofunny:
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    (Original post by the bear)
    this is the math forum, not the "everyday English forum" :toofunny:
    Exactly. The way you're using the word makes more sense in everyday English, but it's not how we use it in mathematics.

    In mathematics, when we talk about "a solution of an equation  f(x) = 0" we mean "a root of  f(x) ". Equivalently, this means "a value of  x that make the equation true."

    This is just a quibble about definitions and standard use - looking it up/asking someone will reveal that I'm correct.
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    in math you can speak loosely of "solutions" when in fact you mean "the solution".
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    (Original post by the bear)
    in math you can speak loosely of "solutions" when in fact you mean "the solution".
    http://www.google.co.uk/search?q=%27...an+equation%27
    Seriously, just look it up. I've even googled it for you...
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    (Original post by studentro)
    http://www.google.co.uk/search?q=%27...an+equation%27
    Seriously, just look it up. I've even googled it for you...
    hey i understand that on this "Google" and "internet" it is considered poor form to express oneself clearly and precisely.
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    (Original post by the bear)
    hey i understand that on this "Google" and "internet" it is considered poor form to express oneself clearly and precisely.
    https://www.google.co.uk/search?q=%2...an+equation%27
    https://www.mathsisfun.com/algebra/e...s-solving.html
    https://www.khanacademy.org/math/cc-...near-equations
    http://www.jamesbrennan.org/algebra/..._equations.htm
    http://www.virtualnerd.com/middle-ma...ion-definition
    https://en.wikipedia.org/wiki/Equation_solving

    If you have decided that the internet cannot be trusted, then find a book or ask a teacher. If you've decided that no external source can be trusted, then there's no point quibbling about the standard way of using words in maths.
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    1 solution

    ≥1 roots

    ftw
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    (Original post by the bear)
    1 solution

    ≥1 roots

    ftw
    You don't have roots of an equation, you have roots of a function.
    The solutions of  f(x) = 0 are precisely the roots of  f(x) .

    This is how we use the word in mathematics. Find me a single source that suggests this is false; I've provided plenty that suggest it is true.
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    (Original post by studentro)
    You don't have roots of an equation, you have roots of a function.
    The solutions of  f(x) = 0 are precisely the roots of  f(x) .

    This is how we use the word in mathematics. Find me a single source that suggests this is false; I've provided plenty that suggest it is true.
    Lol who really cares?
    Is it that important?
    😂🌝


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    have a fight ...
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    (Original post by physicsmaths)
    Lol who really cares?
    Is it that important?
    (Original post by TeeEm)
    have a fight ...
    Sorry about that, I guess we did get a bit carried away!
    It just annoys me when people are wrong about something so easy to verify but stubbornly insist they are correct.
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    (Original post by studentro)
    You don't have roots of an equation, you have roots of a function.
    The solutions of  f(x) = 0 are precisely the roots of  f(x) .

    This is how we use the word in mathematics. Find me a single source that suggests this is false; I've provided plenty that suggest it is true.
    it used to be that a function had zeros... i guess math must have changed.
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    (Original post by the bear)
    it used to be that a function had zeros... i guess math must have changed.
    It's definitely correct that functions can have 'zeros' and that equations can have multiple 'solutions'.

    However, I've done some digging around - there doesn't seem to be a consensus as to whether equations or functions (or both) have 'roots'.

    So in our discussion, 'solutions' is correct but 'roots' may also be correct.
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    (Original post by studentro)
    It's definitely correct that functions can have 'zeros' and that equations can have multiple 'solutions'.

    However, I've done some digging around - there doesn't seem to be a consensus as to whether equations or functions (or both) have 'roots'.

    So in our discussion, 'solutions' is correct but 'roots' may also be correct.
    & it is definitely incorrect to say that equations have zeros.
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    (Original post by studentro)
    It's definitely correct that functions can have 'zeros' and that equations can have multiple 'solutions'.

    However, I've done some digging around - there doesn't seem to be a consensus as to whether equations or functions (or both) have 'roots'.

    So in our discussion, 'solutions' is correct but 'roots' may also be correct.
    Finally....
    Solutions.
    Numbers that work
    Roots
    Answer
    Who cares 😂


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