Definition:Convergent Product/Number Field

Definition
Let $\mathbb K$ be one of the standard number fields $\Q, \R, \C$.

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

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