Concept
Relation d'équivalence
Concepts associés (34)
Intransitivity
In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations. This may include any relation that is not transitive, or the stronger property of antitransitivity, which describes a relation that is never transitive. A relation is transitive if, whenever it relates some A to some B, and that B to some C, it also relates that A to that C.
Euclidean relation
In mathematics, Euclidean relations are a class of binary relations that formalize "Axiom 1" in Euclid's Elements: "Magnitudes which are equal to the same are equal to each other." A binary relation R on a set X is Euclidean (sometimes called right Euclidean) if it satisfies the following: for every a, b, c in X, if a is related to b and c, then b is related to c.
Well-defined expression
In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. A function is well defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if takes real numbers as input, and if does not equal then is not well defined (and thus not a function).
Projection (set theory)
In set theory, a projection is one of two closely related types of functions or operations, namely: A set-theoretic operation typified by the th projection map, written that takes an element of the Cartesian product to the value A function that sends an element to its equivalence class under a specified equivalence relation or, equivalently, a surjection from a set to another set. The function from elements to equivalence classes is a surjection, and every surjection corresponds to an equivalence relation under which two elements are equivalent when they have the same image.