GENERALISED DISTANCES OF SEQUENCES I: B-DISTANCES

Abstract

In this paper, we investigate the B-distances of infinite sequences. For this purpose we use generalized neighbourhood sequences. The general neighbourhood sequences were introduced for measuring distances in digital geometry (Z(n)). We extend their application to sequences, and present an algorithm which provides a shortest path between two sequences. We also present a formula to calculate the B-distance of any two sequences for a neighbourhood sequence B. We also investigate the concept of k-convergent sequences for k is an element of N, that concept is generally weaker than the convergence. We will use the term k-sequence which is a kind of generalization of the concept of 0-sequence. We also show some connection between the B-distances of sequences and the properties of their difference sequences.