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
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“In relation to God, we are like a thief who has burgled the house of a kindly householder and been allowed to keep some of the gold. From the point of view of the lawful owner this gold is a gift; From the point of view of the burglar it is a theft. He must go and give it back. It is the same with our existence. We have stolen a little of God’s being to make it ours. God has made us a gift of it. But we have stolen it. We must return it.”
—Simone Weil (1909–1943)