Order of Formal Power Series?

Question

Please help me with the Definition of $ord(f)$. (Order of Formal Power Series) From my notes from lectuer i have that:

$Ord(f)$ is the largest $i$ such that $f^\alpha = o$, if $|\alpha| = \alpha_1+...+ \alpha_k < i$.

However in Wikipedia For a non-zero formal Laurent series, the minimal integer $n$ such that $a_n \neq 0 $ is called the order of f.

And now im confused :\

Thanks