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