数据库类型和功能_功能和功能类型

数据库类型和功能

功能 (Function)

Suppose, X and Y are two any sets. A relation f from X to Y is said to be a function. If for every x E X there is a unique y E Y such that (x, y) E f. A function is a special case of the relation. The term such as "transformation", "mapping", "correspondence" and "operations" are used as synonyms for "function". The notation f: X → Y.

假设X和Y是两个任意集合。 从X到Y的关系f被认为是一个函数。 如果对于每个x EX都有一个唯一的y EY ，使得(x，y)E f 。 函数是关系的特例。 诸如“变换” ， “映射” ， “对应”和“操作”之类的术语用作“功能”的同义词。 f表示法：X→Y 。

X → Y is used to express f as a function from X to Y. For a function f: X → Y if (x,y) E f then x is called an argument and the corresponding y is called the image of x under f. Instead of writing (x, y) e f, it is customary to write y= f(x) and to call y the values of the function f at x.

X→Y用于将f表示为从X到Y的函数。 对于函数f：X→Y如果(x，y)E f，则x称为自变量，而对应的y称为f下x的图像。 代替写(x，y)ef ，习惯上写y = f(x)并在x处调用y函数f的值。

Example (f) : A -> B

范例(f)：A-> B

• A is called domain of f.

  A称为f的域 。

• B is called codomain of f.

  B称为f的共域 。

• The range is the set containing all images of the elements of an under function f. It is denoted by f(a).

  范围是包含under函数f的元素的所有图像的集合。 用f(a)表示。

• Range of f = { f(n) | x E A}

  f的范围= {f(n)| x EA}

• Range of f C= B codomain

  f C = B共域的范围

功能类型 (Types of functions)

1. Constant function

1.常数函数

The function f defined in a set X such that f(x) = a, xEX, is called a constant function. In other word f: X → Y is a constant function if the range of f consists of only one element. This can be represented by a diagram.

在集合X中定义的函数f使得f(x)= a ， xEX称为常数函数 。 换句话说，如果f的范围仅包含一个元素，则X→Y是常数函数。 这可以用图表表示。

2. One-to-one (injective)

2.一对一(单射)

A mapping f of X into Y is said to be injective or one-to-one mapping. If distinct elements of X have distinct images in Y. It is called injective.

X到Y的映射f 称为单射或一对一映射 。 如果X的不同元素在Y中具有不同的图像。 这称为内射 。

The f: X → Y is a (one-to-one) mapping, if and only if:f(x1) = f(x2) => x1 = x2

f：X→Y是(一对一)映射 ，当且仅当： f(x1)= f(x2)=> x1 = x2

In other words f: X → Y is one-to-one (or injective) mapping, whenever x1 = x2 then,

换句话说，只要x1 = x2，则f：X→Y是一对一(或内射)映射 ，

F(x1) not equals to f(x2), where, x1, x2 belongs to X.

F(x1)不等于f(x2) ，其中x1 ， x2属于X。

Thus a mapping from a set X into a set Y is one-to-one or injective, if each element of Y has at least one element of X mapping into Y.

因此，如果Y的每个元素都具有X的至少一个元素映射到Y，则从集合X到集合Y的映射是一对一或单射的 。

3. Into mapping

3.映射

A mapping f: A → B is said to be into mapping, if f(A) is a proper subset of B. In this case, we say that f maps A into B.

如果f(A)是B的适当子集，则认为映射f：A→B正在映射 。 在这种情况下，我们说f将A映射为B。

4. Onto function (surjective)

4.入门功能(形容词)

If the mapping f: X → Y is such that every element of Y is the image of at least one element of X then the mapping is called an onto or surjective mapping. In other words, the mapping f: X → Y is onto, if given yEY there exists an element xEX such that y = f(x).

如果映射F：X→Y是如：Y的每个元素是X中的至少一个元件的图像，然后该映射被称为上或满射映射 。 换句话说，映射f：X→Y在其上，如果给定yEY，则存在元素xEX ，使得y = f(x) 。

5. One-to-one (Bijective) function

5.一对一(双射)功能

A mapping which is one-to-one as well as onto is called Bijective or one-to-one onto mapping.

一对一以及到一对一的映射称为Bijective或一对一到映射 。

To determine whether a mapping is Bijective, we follow the following procedure.

要确定映射是否为Bijective ，我们遵循以下过程。

• To show that f is one-to-one we must show that

  为了证明f是一对一的，我们必须证明

  f(x1) = f(x2) => x1 = x2

  f(x1)= f(x2)=> x1 = x2

• To show that f is onto we must show that for each yEY, there exists an xEX such that f(x) = y.

  为了证明f在上面，我们必须证明对于每个yEY ，都有一个xEX使得f(x)= y 。

  Then, it is

  那是

  one-to-one onto mapping. The sets X and Y have the same number of elements.

  一对一映射 。 X和Y集具有相同数量的元素。

6. Invertible function

6.可逆功能

A function f: X → Y is said to be invertible. If there exists a function g: y → X such that: Fog = ty and gof = tx

函数f：X→Y被认为是可逆的 。 如果存在函数g：y→X ，使得： Fog = ty和gof = tx

Where Ix and Iy are the identify maps. In such a case the function g is called the inverse of f and is denoted by f^-1.

其中Ix和Iy是标识图。 在这种情况下，函数g称为f的逆，并由f ^ -1表示。

翻译自: https://www.includehelp.com/basics/functions-and-the-types-of-functions.aspx

数据库类型和功能