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Order symbol

  1. Nov 27, 2012 #1
    Hi, I noticed in mathematics the O symbol is used in the following way:

    A term T is in O(x^p), if lim x->0 T/x^p=c, for a constant c.

    While in computer science the O symbol is used is this way:

    A term T is in O(x^p), if lim x->∞ T/x^p is a constant.

    What gives, these two notations seem to be the complete opposite of each other?
  2. jcsd
  3. Nov 27, 2012 #2


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    The O symbol is valid in both cases. It is up to you to define what the x limit is.
  4. Nov 28, 2012 #3
    But don't they contradict each other?

    For example, in the first case x^7 is in O(x^5), but in the second case it is not.
  5. Nov 28, 2012 #4


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    No, they are just two distinct cases of a general concept. We should aways say "f(x)= O(g(x)) as x-> a and specify a. They are using two different values of a and so getting two different results.
  6. Nov 28, 2012 #5
    Aha, thanks!
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