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Thread: Big Oh

  1. #1
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    Big Oh

    If T(n) = O(f(n)) and f(n) = O(g(n)), then T(n) = O(g(n)).
    I have to prove this and need direction. Any tips?
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  2. #2
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    Quote Originally Posted by statman101 View Post
    If T(n) = O(f(n)) and f(n) = O(g(n)), then T(n) = O(g(n)).
    I have to prove this and need direction. Any tips?
    $\displaystyle T(n)=O(f(x))==> |T(n)|\leq M_1|f(n)|\,\,as\,\,n\rightarrow \infty$ ,

    $\displaystyle f(n)=O(g(n))\Longrightarrow |f(n)|\leq M_2|g(n)|\,\,as\,\,n\rightarrow\infty$ ,

    $\displaystyle M_1,M_2$ constants, so

    $\displaystyle |T(n)|\leq M_1M_2|g(n)|$...and etc.

    Tonio
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