Definition:Convergent Product/Arbitrary Field

Definition
Let $\struct {\mathbb K, \norm {\,\cdot\,} }$ be a valued field.

Arbitrary Sequence
The product is said to be convergent to $a$, and one writes:
 * $\displaystyle \prod_{n \mathop = 1}^\infty a_n = a$

A product is thus convergent it converges to some $a \in \mathbb K$.