synonym

Shine light on objects: plants need sunlight.

Reflective lighting: Xia Guang reflection.

Mapping is a mathematical term that refers to the relationship between elements of two sets.

It is often equivalent to a function in mathematics and related fields. Based on this, partial mapping is equivalent to partial function, and complete mapping is equivalent to complete function.

Conditions of establishment

The simple expression of the mapping condition is:

Ergodicity of 1. domain: Every element X in X has a corresponding object in the mapping range.

2. Uniqueness of correspondence: one element in the definition domain can only correspond to one element in the mapping range.

Classified editing

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Different mapping classification is based on the mapping results, from the following three angles:

1. According to the geometric properties of the results, they are classified as surjective (top) and non-surjective (inside).

2. According to the analytical nature of the results, they are divided into injective (one by one) and non-injective.

3. Consider the geometric and analytical properties: complete injection capacity (one-to-one correspondence).

Applied editing

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

If we extend the two sets in the function definition from non-empty sets to sets of arbitrary elements (not limited to numbers), we can get the concept of mapping: mapping is a term in mathematics that describes a special correspondence between two sets of elements.

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

(1) Let A={ 1, 2, 3, 4} and B={3, 5, 7, 9}, and the element X in set A corresponds to the element in set B according to the corresponding relationship, which is the mapping from set A to set B.

(2) 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. ..