Definition:Absolute Convergence of Product/General Definition/Definition 1

Definition
Let $\mathbb K$ be a field with absolute value $\left\vert{\cdot}\right\vert$.

Let $(a_n)$ be a sequence in $\mathbb K$.

Then the infinite product $\displaystyle \prod_{n \mathop = 1}^\infty \left({1 + a_n}\right)$ is absolutely convergent $\displaystyle \prod_{n \mathop = 1}^\infty \left({1 + \left\vert{a_n}\right\vert}\right)$ is convergent.