STRUCTURE AND PROPERTIES OF APPROXIMATE FUNCTIONS FROM COLLAPSING BOUNDARIES AND THE ANALOGY OF HUMAN RELATIONSHIPS

Abstract

The paper explores structure and properties of pairs and faster pairs of approximate functions from collapsing boundaries of a positive series. It relates results from Mathematics of approximate functions to human relationship using analogies and suitable keys. It likens the mathematical search for faster pairs to breaking friendship boundaries and setting new boundaries or seeking new friends towards satisfying desired goals or timely expectations. It asserts among other things: Every collapsing boundary friend is a product of a compliant and non-compliant part, Amenable friends of collapsing boundaries can be converted in some activities, children of friends may not be friends of one’s children, if they become friends, it is possible to have closer relationship than their parents. Analysis of the error term led to an accidental discovery from a simulation calculation that if the error term tend to zero as (n) tends to infinity, the square root functions are 1-subtractive square root of rational number equivalence. The discovery prompted further investigation on the conditions for 1-subtractiveness, its role in the convergence of square root function inclusions in error terms of the approximate functions, and a general proof that the square root function inclusions in error terms of pairs of approximate functions from collapsing boundaries are 1-subtractive square root of rational number equivalence. Thus 1-subtactiveness is a useful characterization of square root function inclusions in error terms of approximate functions from collapsing boundaries. The paper also
illustrate how to use the concept of one subtractiveness to construct approximate of a given function of (n) when n is large.