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Math Help - BIG O proof

  1. #1
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    Question BIG O proof

    How do I prove the following:
    O(n^2 logn) is also O(n^3)?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by taurus View Post
    How do I prove the following:
    O(n^2 logn) is also O(n^3)?
    f(n)\in O(n^2 \log(n))

    means there exists a constant k>0 and an N>0 such that for all n>N:

    |f(n)|<k n^2 \log(n)

    Now for n>0 we have n>\log(n) so for n>N>0:

    |f(n)|<k n^3

    etc.

    CB
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  3. #3
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    You will have to expand on that, I have no clue how to go on...
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by CaptainBlack View Post
    f(n)\in O(n^2 \log(n))

    means there exists a constant k>0 and an N>0 such that for all n>N:

    |f(n)|<k n^2 \log(n)

    Now for n>0 we have n>\log(n) so for n>N>0:

    |f(n)|<k n^3

    etc.

    CB
    Quote Originally Posted by taurus View Post
    You will have to expand on that, I have no clue how to go on...
    So there exists a constant k>0 and an N>0 such that for all n>N:

    |f(n)|<k n^3

    hence f(n)\in O(n^3)

    CB
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