\begin{definition}[Definition:Convergent Product/Number Field/Nonzero Sequence]
Let $\mathbb K$ be one of the standard number fields $\Q, \R, \C$.
Let $\sequence {a_n}$ be a sequence of nonzero elements of $\mathbb K$.
Then:
:The infinite product $\ds \prod_{n \mathop = 1}^\infty a_n$ is '''convergent'''
{{iff}}:
:its sequence of partial products converges to a nonzero limit $a \in \mathbb K \setminus \set 0$.
Category:Definitions/Infinite Products
\end{definition}