What Is Outcome Mapping?

In mathematics, mapping is a term that refers to the "corresponding" relationship between elements in a set of two elements, as a noun. Mapping , or projective , is often equivalent to function in mathematics and related fields. Based on this, a partial mapping is equivalent to a partial function, and a full mapping is equivalent to a full function.

Two

The simple formulation of the mapping conditions is:

1.

The number of elements in the set AB is m, n,

Then, the number of mappings from set A to set B is

.

The difference between functions and mappings, full mappings and single mappings.

The function is a set-to-set mapping, and this mapping is "full".

That is, the full map f: A B is a function, in which the original image set A is called the domain of the function, and the image set B is called the range of the function.

A "number set" is a collection of numbers, which can be integers, rational numbers, real numbers, complex numbers, or part of them.

"Mapping" is a broader mathematical concept than a function. It is a certain correspondence between a set and another set. That is, if f is a mapping from set A to set B, then for any element a in A, there is a unique element b in set B that corresponds to a. We call a a primary image and b an image. Write f: A B, the element relationship is b = f (a).

A mapping f: A B is called "full", that is to say, for all elements in B, there exists in A

The different classifications of the mapping are based on the mapping results, and are performed from the following three perspectives:

1. Classification based on the geometric properties of the results:

In many specific mathematical fields, this term is used to describe functions with specific properties associated with the field, such as continuous functions in topology, linear transformations in linear algebra, and so on. In formal logic, the term is sometimes used to represent functional predicates, where functions are models of predicates in set theory.

If two sets in a function definition are expanded from a non-empty set to a set of arbitrary elements (not limited to numbers), we can get the concept of mapping: mapping is a mathematical description of a special correspondence between two set elements A term.

According to the definition of mapping , the following correspondences are mappings .

(1) Let A = {1,2,3,4} and B = {3,5,7,9}. The element x in set A corresponds to the element multiply 2 plus 1 and the element in set B corresponds to This correspondence is a mapping from set A to set B.

(2) Let A = N *, B = {0,1}, the elements in set A correspond to the elements in set B according to the corresponding relationship the remainder obtained by dividing x by 2, and this correspondence is from set A to set B Mapping.

(3) Let A = {x | x is a triangle}, B = {y | y> 0}, the element x in set A corresponds to the element in set B according to the corresponding relationship calculated area, and this correspondence is set A Mapping to set B.

(4) Let A = R and B = {points on a straight line}. According to the method of establishing the number axis, the number x in A corresponds to the point P in B, and this correspondence is the mapping from set A to set B.

(5) Let A = {P | P be a point in the rectangular coordinate system}, B = {(x, y) | xR, yR}, according to the method of establishing a plane rectangular coordinate system, it is in Point P corresponds to the ordered real number pair (x, y) in B, and this correspondence is the mapping from set A to set B.

For "mapping" or "projection", it is necessary to define functions in the projection rule before performing operations. Therefore, the "mapping" calculation can achieve cross-dimensional correspondence. The corresponding calculus is a purely digital calculation that cannot achieve cross-dimensional correspondence. Using differential simulation can achieve complex simulations in this dimension. Mapping can perform corresponding approximate operations on unrelated multiple sets, while calculus can only perform accurate operations on a large set that is continuously related.