1. ## BIG O proof

How do I prove the following:
O(n^2 logn) is also O(n^3)?

2. Originally Posted by taurus
How do I prove the following:
O(n^2 logn) is also O(n^3)?
$\displaystyle f(n)\in O(n^2 \log(n))$

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

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

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

$\displaystyle |f(n)|<k n^3$

etc.

CB

3. You will have to expand on that, I have no clue how to go on...

4. Originally Posted by CaptainBlack
$\displaystyle f(n)\in O(n^2 \log(n))$

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

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

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

$\displaystyle |f(n)|<k n^3$

etc.

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

$\displaystyle |f(n)|<k n^3$

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

CB