Double sequence

Summary

A double sequence is a family $(x_{m,n})$ indexed by pairs of natural numbers, like an infinite matrix. It has several notions of limit. There is the joint limit as $m$ and $n$ both grow, and there are two iterated limits taken one index at a time. These limits can differ, and theorems such as the Moore–Osgood theorem say when they agree. The exact definition is in double sequence.