Compatible Operation
Let A be a set (of the elements of an algebra ), and let E be an equivalence relation on the set A. The relation E is said to be compatible with (or have the substitution property with respect to) an n-ary operation f if for all whenever implies . An equivalence relation compatible with all the operations of an algebra is called a congruence.
Read more about this topic: Quotient Algebra
Famous quotes containing the words compatible and/or operation:
“English general and singular terms, identity, quantification, and the whole bag of ontological tricks may be correlated with elements of the native language in any of various mutually incompatible ways, each compatible with all possible linguistic data, and none preferable to another save as favored by a rationalization of the native language that is simple and natural to us.”
—Willard Van Orman Quine (b. 1908)
“Human knowledge and human power meet in one; for where the cause is not known the effect cannot be produced. Nature to be commanded must be obeyed; and that which in contemplation is as the cause is in operation as the rule.”
—Francis Bacon (1560–1626)