Abstract
This chapter discusses the different aspects of residuation theory. It presents an assumption where E is a set and R is a binary relation between elements of E. R is said to be reflexive if (V x ∈ E) xRx. A relation that satisfies condition is called an equivalence relation on E. The only binary relation on a set E that is both an equivalence relation and an ordering on E is the relation of equality. The set P(E) of all subsets of a set E is an ordered set under the relation ⊆ of set inclusion. A set E is totally ordered if it is ordered in such a way that for any given elements x, y ∈ E one has x < y or y < x. The relations x ≰ y and y < x are equivalent only in the case of a totally ordered set and not in the general case of an ordered set.
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