Notes on providing a formal definition of equivalence

This paper presents an outline of the definition of equivalence in mathematics. The supporting language of set theory is informally presented. Definitions are provided for Cartesian product, relation and equivalence relation. Equivalence classes and partitions are touched on, though they are not developed in detail. The exposition is presented with brief examples which are drawn from the world of numbers, objects and people in order to illuminate the definitions. The examples are not belabored or complete; the intent is to provoke thinking about the process of creating the definitions that are necessary to impose the formal structures of mathematics.