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Math Help - [SOLVED] Notation

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

    What does \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 x^{(0)}?
    Last edited by garymarkhov; March 16th 2010 at 12:28 PM.
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  2. #2
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    Quote Originally Posted by garymarkhov View Post
    What does \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 x^{(0)}?
    \max\{a,b\} means the larger of the numbers a and b.
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  3. #3
    Member garymarkhov's Avatar
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    Quote Originally Posted by Opalg View Post
    \max\{a,b\} means the larger of the numbers a and b.
    Thanks. And do you know if x^{(0)} has any special meaning distinct from x^{0} ?
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  4. #4
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    Quote Originally Posted by garymarkhov View Post
    Thanks. And do you know if x^{(0)} has any special meaning distinct from x^{0} ?
    That would depend on the context. As far as I know, there is no standard meaning for superscripts in parentheses, as in x^{(0)}.
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  5. #5
    Member mathemagister's Avatar
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    Quote Originally Posted by garymarkhov View Post
    Thanks. And do you know if x^{(0)} has any special meaning distinct from x^{0} ?
    As a side note: in general convention, if you see x^{(n)} where 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 x^{(n)} where 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 x^{(0)} would be the first term of some sequence (x^{(k)})_{k\in\mathbb{N}}.
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