I'm reading Cassels & Frohlich's book Algebraic Number Theory. On page 2, it has the following example:
Let $F$ be a field and let $K$ be the field of formal series $$\sum_{n=-\infty}^{\infty}a_nt^n$$ where $a_n \in F$ and $m \in \mathbb{Z}$. Then we have a standard discrete valuation $v$ of $K$ given by $$v(\sum_{n=-\infty}^{\infty}a_nt^n):=\inf \{n \in \mathbb{Z} \mid a_n \neq 0\}$$ $K$ is complete in the valuation topology.
Can anyone explain to me why is $K$ complete?