I am currently reading about the subject given in the title of this thread. The definition they give for equivalence classes in my textbook is a rather ostentatious in its wording, so I just want to make certain that I am understanding it properly. They say to let R be an equivalence relation on a set A, meaning that this this particular relation is reflexive, symmetric, and transitive, right? Essentially the rest of it seems to say that you can partition off the elements that make the relation reflexive, thereby creating a subset of the relation R. Does that seem right?
I could really use some help, thank you!