growth function

**galactus** · February 2nd 2009, 10:08 AM

Hey All:

I am not sure where to post something like this.

I have encountered something I am not familiar with too well.

This is part of

determine rather this is true or not:

$f(n)\in {\Theta}(n^{3})$

$f(n)\in {\Omega}(n^{2})$

What does this stuff represent?.

Anyone have an idea?.

The theta is the asymptotic tight bound and the Omega is the asymptotic lower bound.

**Laurent** · February 3rd 2009, 07:45 AM

Originally Posted by galactus

Hey All:

I am not sure where to post something like this.

I have encountered something I am not familiar with too well.

This is part of

determine rather this is true or not:

$f(n)\in {\Theta}(n^{3})$

$f(n)\in {\Omega}(n^{2})$

What does this stuff represent?.

Anyone have an idea?.

The theta is the asymptotic tight bound and the Omega is the asymptotic lower bound.

You'll find every answer and more in this wikipedia article

In a word, $f(n)= \Omega(g(n))$ means " $g(n)= O(f(n))$ " (and I had never seen it before), while $f(n)= \Theta(g(n))$ means " $f(n)= O(g(n))$ and $g(n)= O(f(n))$ ". In math, I think the notation $f(n)\asymp g(n)$ is more common than $f(n)=\Theta(g(n))$ .

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