Definition:Convergent Product/Number Field/Nonzero Sequence

Definition
Let $\mathbb K$ be one of the standard number fields $\Q, \R, \C$. Let $\sequence{a_n}$ be a sequence of nonzero elements of $\mathbb K$.

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