Equivalence Relations
In this sequence of lectures, we're going to connect relations back to the partitions we talked about in our discusion of set theory. As we'll see, partitions and equivalence relations are equivalent to each other in the sense that one of them alwayw generates the other.
Videos
In this series of lectures, we're going to look at the relationship between relations and partitions starting off with examples of relations that are "induced" by a partition. (lecture slides)
In this lecture, we're going to look at several examples of "equivalence classes" - subsets of the base set that are created by an equivalence relation. (lecture slides)
This brings us to the main theoretical point of the chapter: the distinct equivalence classes of an equivalence relation are a partition of the underlying set. (lecture slides)
