Give examples of two continuous functions $f(n)$ and $g(n)$ of positive real inputs $n$, such that
- $f(n)$ not equal to $O(g(n))$,
- $g(n)$ not equal to $O(f(n))$,
- $f(n)$ not equal to $Omega(g(n))$ and
- $g(n)$ not equal $omega(f(n))$.
Hint: You can specify some of the values of $f(n)$ and/or $g(n)$ depending on some condition on $n$, such as when $n$ is even or odd, but make sure that your function is continuous and defined for all positive real $n$.