In this paper we define derived sequences <x|sigma> and <sigma |\n x> for a real number x and a real sequence sigma which allow us to\n decide when x shall be ``near\'\' sigma or `` far from\'\'sigma.\n In this setting the concepts `` somewhat near sigma\'\' and `` somewhat\n far from sigma\'\' are naturally\n definable and seen to be non-naturally\n exclusive.\n Building on these\n observations several results are proved as theorems and\n propositions, while in a section of remarks and examples an outline of an\n alternative analysis is sketched in order to provide the reader\n better insight into the intuitive meaning of the ideas developed\n here. The squared Riemann-zeta function is observed to be related\n to the sequence of prime in this setting as well.