I have to find two functions $f(n)$ and $g(n)$
criteria for $f(n)$ are:
- $f(n) \in O(n \cdot \log(n))$
- $f(n) \notin Θ(n \cdot \log(n))$
criteria for $g(n)$ are:
- $g(n) \in Ω(n)$
- $g(n) \notin Θ(n)$
I'm new to this, so this might be a trivial problem. But I just can't find a solution. I know:
$f(n) \in O(g(n)) \iff 0\le \limsup\limits_{n\rightarrow\infty} \frac{f(n)}{g(n)} \lt \infty$
$f(n) \in Θ(g(n)) \iff 0\lt \lim\limits_{n\rightarrow\infty} \frac{f(n)}{g(n)} \lt \infty$
$f(n) \in Ω(g(n)) \iff 0\lt \liminf\limits_{n\rightarrow\infty} \frac{f(n)}{g(n)} \le \infty$