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 $\mathbb K$.

Then:
 * The infinite product $\ds \prod_{n \mathop = 1}^\infty a_n$ is convergent


 * its sequence of partial products converges to a nonzero limit $a \in \mathbb K \setminus \set 0$.
 * its sequence of partial products converges to a nonzero limit $a \in \mathbb K \setminus \set 0$.