The primary purpose of this paper is to introduce the notion of double sequences in 2-normed space. We provide a simple way to derive a norm from the standard 2-norm by using double sequences when a 2-normed space is given. Equivalence relation between derived norm and the usual norm are established. Using this derived norm, we examine the completeness property of a 2-normed space and we extend the results to n-normed spaces.

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