Definition:Convergent Product/Arbitrary Field/Nonzero Sequence

Definition
Let $\struct {\mathbb K, \size{\,\cdot\,}}$ be a valued field. Let $(a_n)$ be a sequence of nonzero elements of $\mathbb K$.

The infinite product $\displaystyle \prod_{n \mathop = 1}^\infty a_n$ is convergent its sequence of partial products converges to a nonzero limit $a\in\mathbb K\setminus\{0\}$.