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Thread: [SOLVED] Notation

  1. #1
    Member garymarkhov's Avatar
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    [SOLVED] Notation

    What does $\displaystyle \frac{| \tilde x^{(0)} - x^{(0)} | } {max \lbrace 1, | x^{(0)} | \rbrace} \ge \epsilon $ mean, particularly the comma in the denominator? And do the brackets have any special meaning wrt the $\displaystyle x^{(0)}$?
    Last edited by garymarkhov; Mar 16th 2010 at 12:28 PM.
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    Quote Originally Posted by garymarkhov View Post
    What does $\displaystyle \frac{| \tilde x^{(0)} - x^{(0)} | } {max \lbrace 1, | x^{(0)} | \rbrace} \ge \epsilon $ mean, particularly the comma in the denominator? And do the brackets have any special meaning wrt the $\displaystyle x^{(0)}$?
    $\displaystyle \max\{a,b\}$ means the larger of the numbers a and b.
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    Member garymarkhov's Avatar
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    Quote Originally Posted by Opalg View Post
    $\displaystyle \max\{a,b\}$ means the larger of the numbers a and b.
    Thanks. And do you know if $\displaystyle x^{(0)}$ has any special meaning distinct from $\displaystyle x^{0}$ ?
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    Quote Originally Posted by garymarkhov View Post
    Thanks. And do you know if $\displaystyle x^{(0)}$ has any special meaning distinct from $\displaystyle x^{0}$ ?
    That would depend on the context. As far as I know, there is no standard meaning for superscripts in parentheses, as in $\displaystyle x^{(0)}$.
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    Quote Originally Posted by garymarkhov View Post
    Thanks. And do you know if $\displaystyle x^{(0)}$ has any special meaning distinct from $\displaystyle x^{0}$ ?
    As a side note: in general convention, if you see $\displaystyle x^{(n)}$ where $\displaystyle n \ge 4$, it represents the nth derivative of x.
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  6. #6
    Member garymarkhov's Avatar
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    Quote Originally Posted by mathemagister View Post
    As a side note: in general convention, if you see $\displaystyle x^{(n)}$ where $\displaystyle n \ge 4$, it represents the nth derivative of x.
    Interesting, thanks.
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  7. #7
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    It is also often used for sequences.

    That is $\displaystyle x^{(0)}$ would be the first term of some sequence $\displaystyle (x^{(k)})_{k\in\mathbb{N}}$.
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