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Homework Help: Asymptotic Notation

  1. Feb 19, 2008 #1
    Suppose f(N) = O(h(N)) and g(N) = O(h(N))

    1. Is f(N) + g(N) = O(h(N))
    2. Is f(N) * g(N) = O(h(N))

    Justify answers

    I am totally lost on these questions. ANY help would be greatly appreciated.
     
  2. jcsd
  3. Feb 19, 2008 #2
    This is the Big-O Notation. It is involved in comparing the growth of one number-theoretic function with that of another. There is a sequence of these functions. For instance:

    [tex] f_2 = log_2 n [/tex]
    .
    .
    .
    [tex] f_{7.2} = n^2 [/tex]
    [tex] f_{7.3} = n^3 [/tex]
    .
    .
    .
    [tex] f_{7.k} = n^k [/tex]
    .
    .

    Now answer these questions:

    Does adding [tex] n^2 [/tex] to [tex] n^2 [/tex] change the level in the sequence?
    How about multiplying? (different constants don't count)
     
    Last edited: Feb 19, 2008
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