\begin{definition}[Definition:Convergent Product/Arbitrary Field/Nonzero Sequence]
Let $\struct {\mathbb K, \norm {\,\cdot\,} }$ be a valued field.
Let $\sequence {a_n}$ be a sequence of nonzero elements of $\mathbb K$.
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}