\begin{definition}[Definition:Sequence/Doubly Subscripted]
A '''doubly subscripted sequence''' is a mapping whose domain is a subset of the cartesian product $\N \times \N$ of the set of natural numbers $\N$ with itself.
It can be seen that a '''doubly subscripted sequence''' is an instance of a family of elements indexed by $\N^2$.
A '''doubly subscripted sequence''' can be denoted $\left\langle{a_{m n} }\right\rangle_{m, \, n \mathop \ge 0}$
\end{definition}