Is $O(\frac{1}{n}) = o(1)$? Sorry about yet another big-Oh notation question, I just found it very confusing.
If $T(n)=\frac{5}{n}$, is it true that $T(n)=O(\frac{1}{n})$ and $T(n) = o(1)$? I think so because (if $h(n)=\frac{1}{n}$) 
$$
\lim_{n \to \infty} \frac{T(n)}{h(n)}=\lim_{n \to \infty} \frac{\frac{5}{n}}{\frac{1}{n}}=5>0 ,
$$
therefore $T(n)=O(h(n))$. 
At the same time (if $h(n)=1$)
$$
\lim_{n \to \infty} \frac{T(n)}{h(n)}=\frac{(\frac{5}{n})}{1}=0,
$$
therefore $T(n)=o(h(n))$.
Thanks!

$\frac{1}{n}=o(1)$ and therefore if $f=O(\frac{1}{n})$ than $f=o(1)$.
