Let a and b be two groups. If there is a unique element in set B that corresponds to any element in set A according to a certain correspondence F, then such correspondence (including sets A and B, and the correspondence F from set A to set B) is called the mapping from set A to set B, which is denoted as F: A → B.
According to the definition of mapping, the following mappings are all mappings.
(1) Let A={ 1, 2, 3, 4} and B={3, 4, 5, 6, 7, 8, 9}, and the element X in the set A corresponds to the element 2x+ 1 in the set B according to the corresponding relationship, corresponding to the sets A to.
⑵ Let A=N*, B={0, 1}, and the elements in set A correspond to the elements in set B according to the corresponding relation "the remainder obtained by dividing X by 2", which is the mapping from set A to set B.
(3) Let A={x|x is a triangle} and B = {y | y & gt0}, and the element X in set A corresponds to the element in set B according to the correspondence, which is the mapping from set A to set B. ..
(4) Let A=R and B={ Point is 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, which is the mapping from set A to set B..
5] Let A={P|P is a point in a rectangular coordinate system} B = {(x, y)|x∈R, y∈R}. According to the method of establishing plane rectangular coordinate system, the point P in A corresponds to the ordered real number pair (x, y) in B, and this correspondence is the mapping from set A to set B..
Given a mapping from set A to set B, and a∈A and b∈B, if element A and element B correspond, then we call element B the image of element A and element A the original image of element B.
Mapping describes the special correspondence between two set elements in mathematics.
Mapping has many names in different fields, and its essence is the same. Such as functions, operators and so on. What needs to be explained here is that a function is a mapping between two data sets, and other mappings are not functions.