Study of Relations’ Properties Compatibility

Abstract

This article is a sequel of my earlier paper [1]. In the 1^st section the conditions for emergence of tolerance are considered – the uncertainty in definition of diagonal for such sets leads to it. Furthermore it was shown that relations’ property manifestations described earlier cannot appear accidentally and independently on each other. Also it was shown that just reflexive antisymmetric transitive relations may be applicable to make set ordering. Further an ambiguity in definition of idempotent element amongst relations was presented. General definitions of set theory (such as ordered and unordered pairs, set union and intersection etc.) are detailed in the works [6 – 14].