Search results
Results From The WOW.Com Content Network
Given a function :, the canonical surjection of f onto its image () = {()} is the function from X to f(X) that maps x to f(x). For every subset A of a set X , the inclusion map of A into X is the injective (see below) function that maps every element of A to itself.
A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
Self-concordant function; Semi-differentiability; Semilinear map; Set function; List of set identities and relations; Shear mapping; Shekel function; Signomial; Similarity invariance; Soboleva modified hyperbolic tangent; Softmax function; Softplus; Splitting lemma (functions) Squeeze theorem; Steiner's calculus problem; Strongly unimodal ...
Depending on the value of μ, the tent map demonstrates a range of dynamical behaviour ranging from predictable to chaotic. If μ is less than 1 the point x = 0 is an attractive fixed point of the system for all initial values of x i.e. the system will converge towards x = 0 from any initial value of x. If μ is 1 all values of x less than or ...
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
An animated cobweb diagram of the logistic map = (), showing chaotic behaviour for most values of >. A cobweb plot , known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions , such as the logistic map .
One has always X ⊆ f −1 (f(X)) and f(f −1 (Y)) ⊆ Y, where f(X) is the image of X and f −1 (Y) is the preimage of Y under f. If f is injective, then X = f −1 (f(X)), and if f is surjective, then f(f −1 (Y)) = Y. For every function h : X → Y, one can define a surjection H : X → h(X) : x → h(x) and an injection I : h(X) → Y ...
Namely, given a surface X in Euclidean space R 3, the Gauss map is a map N: X → S 2 (where S 2 is the unit sphere) such that for each p in X, the function value N(p) is a unit vector orthogonal to X at p. The Gauss map is named after Carl F. Gauss. The Gauss map can be defined (globally) if and only if the surface is orientable, in which case ...