Definition:Sequence/Doubly Subscripted

Definition
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 $\left\langle{a_{m n} }\right\rangle_{m, \, n \mathop \ge 0}$