ABSTRACT
This chapter introduce three properties of abstract relations that are based on corresponding properties of logical equality: reflexivity, symmetry, and transitive. It presents theorems that describe the properties of reflexivity, symmetry, and transitivity. The abstract definition of an equivalence relation gives a precise mathematical formulation of various intuitive notions of equivalence. The chapter defines equivalence relations and considers many examples, including congruence of integers modulo and the equivalence relation induced by a function. It introduces set partitions, which are ways of dividing a given set into collections of non-overlapping subsets, and discusses the bijection between equivalence relations and set partitions. The chapter formulates the abstract concept of ordering by singling out appropriate properties of the concrete ordering relation on real numbers.
