Double sequence

A sequence of certain elements numbered by two indices:

As compared to ordinary sequences (i.e. sequences numbered with the aid of one index), double sequences have a number of distinguishing features; thus, there are several definitions of the limit of a double sequence which are not mutually equivalent.

The concept of a numerical double sequence is closely connected with that of a numerical double series

both the terms and the (rectangular) partial sums of such a double series,

constitute a double sequence. See also Double series.

Comments

A double sequence for which the notion of its limit causes trouble is given by, e.g.,

Letting for fixed, and subsequently gives as limit 1. On the other hand, letting for fixed, and subsequently gives 0.

See also Double limit; Repeated limit.