In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent (with respect to the equivalence relation) if and only if they are elements of the same cell. The intersection of any two different cells is empty; the union of all the cells equals the original set.
Read more about Equivalence Relation: Notation, Definition, Connections To Other Relations, Well-definedness Under An Equivalence Relation, Fundamental Theorem of Equivalence Relations, Comparing Equivalence Relations, Generating Equivalence Relations, Algebraic Structure, Equivalence Relations and Mathematical Logic, Euclidean Relations
Famous quotes containing the word relation:
“To criticize is to appreciate, to appropriate, to take intellectual possession, to establish in fine a relation with the criticized thing and to make it one’s own.”
—Henry James (1843–1916)