Definition of function: Let A and B be two sets of non-empty numbers. According to some corresponding rule F, for each number X in set A, there is a unique number corresponding to it in set B.. This correspondence is called a function from a to b, and is usually expressed as y = f (x) and x ∈ a. ..
Definition of mapping: Let A and B be two nonempty sets. If any element in set A has a unique element corresponding to it in set B according to some corresponding rule F, then such a single-valued correspondence is called a mapping from A to B, which is usually recorded as
F: A- > B.
Extended data:
Different mapping classification is based on the mapping results, from the following three angles:
1, classified according to the geometric properties of the results: surjective and non-surjective.
2. According to the analytical nature of the results, they are divided into injective and non-injective.
3. Consider the geometric and analytical properties: complete injection capacity (one-to-one correspondence).
Functional classification:
An injective function that maps different variables to different values.
The range of a injective function is its corresponding range. That is, for any Y in the mapping domain of mapping F, there is at least one X that satisfies y=f(x).
A bijection function is both injective and injective. Also called one-to-one correspondence. Bijective function is often used to indicate that sets X and Y are equipotential, that is, they have the same cardinality. If two sets can establish a one-to-one correspondence, they are said to be equipotential.
References:
Baidu encyclopedia-map
References:
Baidu Encyclopedia-Function