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What is "a function must be a mapping, and a mapping is not necessarily a function"
Function is a special kind of mapping, which requires that the elements in two sets must be numbers, while the elements in two sets in the mapping are arbitrary mathematical objects.

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