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Math Help - What does "arrow down" mean?

  1. #1
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    Question What does "arrow down" mean? [SOLVED]

    Hi all.

    I need some help to understand this, what should be simple, sentence:

    Since a \to b as c \downarrow 0 it was shown that...


    What does the down arrow mean? It can not mean "goes to", since c is a constant. I'm thinking it is meaning something like "c is a small positive number" ??

    Thanks.
    Last edited by julle; May 17th 2011 at 12:45 AM.
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  2. #2
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    Quote Originally Posted by julle View Post
    Since a \to b as c \downarrow 0 it was shown that...[/I]
    What does the down arrow mean? It can not mean "goes to", since c is a constant. I'm thinking it is meaning something like "c is a small positive number" ??
    That is limit from the right, from above: \lim _{x \to c^ +  } f(x) = \lim _{x \downarrow c} f(x).
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  3. #3
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    Thanks for reply. Not sure I understand, though.

    If it is the same, why should the author use two different arrows in the same expression?
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  4. #4
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    Quote Originally Posted by julle View Post
    Thanks for reply. Not sure I understand, though. If it is the same, why should the author use two different arrows in the same expression?
    They are not the same, I did not say they were.

    a \to b as c \downarrow 0 is read "a approaches b as c approaches 0 from the right."

    Some authors use \lim _{x \to c^ +  } (note is + in the exponent on c).
    While others use \lim _{x \downarrow c} .
    Now those have the same meaning.
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  5. #5
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    Okay, thanks.

    One last thing: What does "from the right" mean? Does "from the right" equal the positive numbers, and "from the left" equals negative numbers?

    Edit:
    That makes sense, since c never is negative.

    Thanks for your help.
    Last edited by julle; May 17th 2011 at 12:44 AM.
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