A simple proof of the triangle inequality for the NTV metric

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Abstract

We study a certain metric d on Rn that was recently introduced by Nieto, Torres and Vázquez-Trasande [1], give a simple proof for the triangle inequality, and describe when exactly d(p, q) = d(p, r) + d(r, q) holds for some p, q, r ϵ Rn. Remarkably, one has d(p, q) = 2 for some p, q ϵ Rn if and only if 0 = p + qp holds, in which case, one has also d(p, q) = d(p, r) + d(r, q) for all r ϵ R.

Keywords

Metrics
NTV-metric
Triangle inequality
Geodesics
Fuzzy polynucleotides

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