ABSTRACT
An equivalence relation is a mathematical way to describe “sameness.” Consider, for example, the set of lower and upper case letters of the alpha-
bet, (a, b, c, … A, B, C …). You may wish, for some purposes, to think of e and E as the “same” as each other; for other purposes, you may wish to think of the lower case letters as the “same” as each other and for yet other purposes, you may wish to think of vowels as the “same” as each other. When two things are the “same” in some way, in that they share some particular property, they are called “equivalent” with regard to that property. The notion of an equivalence relation provides a means of discussing this abstractly, without referring to any particular property.
