Definition:Convergent Product/Arbitrary Field/Nonzero Sequence

Definition

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