# Definition:Sequence/Doubly Subscripted

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

## Also see

- Results about
**sequences**can be found here.

## Sources

- 1997: Donald E. Knuth:
*The Art of Computer Programming: Volume 1: Fundamental Algorithms*(3rd ed.) ... (previous) ... (next): $\S 1.2.9$: Generating Functions: Exercise $12$