Search results
Results From The WOW.Com Content Network
A function [d] A relation that is functional and total. For example, the red and green relations in the diagram are functions, but the blue and black ones are not. An injection [d] A function that is injective. For example, the green relation in the diagram is an injection, but the red, blue and black ones are not. A surjection [d]
The equivalence relations on any set X, when ordered by set inclusion, form a complete lattice, called Con X by convention. The canonical map ker : X^X → Con X, relates the monoid X^X of all functions on X and Con X. ker is surjective but not injective. Less formally, the equivalence relation ker on X, takes each function f : X → X to its ...
Formally, given a set and an equivalence relation on , the equivalence class of an element in is denoted [] or, equivalently, [] to emphasize its equivalence relation . The definition of equivalence relations implies that the equivalence classes form a partition of S , {\displaystyle S,} meaning, that every element of the set belongs to exactly ...
For example, the red and green binary relations in the diagram are functions, but the blue and black ones are not. An injection: a function that is injective. For example, the green relation in the diagram is an injection, but the red one is not; the black and the blue relation is not even a function. A surjection: a function that is surjective ...
The one-argument function Frege generalizes into the form Φ(A) where A is the argument and Φ( ) represents the function, whereas the two-argument function he symbolizes as Ψ(A, B) with A and B the arguments and Ψ( , ) the function and cautions that "in general Ψ(A, B) differs from Ψ(B, A)".
A multivariate function, multivariable function, or function of several variables is a function that depends on several arguments. Such functions are commonly encountered. For example, the position of a car on a road is a function of the time travelled and its average speed.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Every class whose elements are sets, with the relation ∈ ("is an element of"). This is the axiom of regularity. The nodes of any finite directed acyclic graph, with the relation R defined such that a R b if and only if there is an edge from a to b. Examples of relations that are not well-founded include: