有序对与笛卡尔积(Ordered pair and Cartesian product)

一,有序对与笛卡尔积;

1,定义;第一个元素出现在每个子集合中 , 第二个元素只出现在一个子集合中 , 通过这种方式 , 保证了有序对的定义 , 一前一后两个元素 , 前后顺序不同 , 对应的有序对不同 ;

下面是相同的两个元素的不同的有序对 :

有序对 < a , b > = { { a } , { a , b } } <a, b> = \{ \{ a \} , \{ a , b \} \}<a,b>={{a},{a,b}}

有序对 < b , a > = { { b } , { a , b } } <b, a> = \{ \{ b \} , \{ a , b \} \}<b,a>={{b},{a,b}}2,笛卡尔积

令A和B是任意两个集合,若序偶的第一个成员是A的元素,第二个成员是B的元素,所有这样的序偶集合,称为集合A和B的笛卡尔乘积或直积,记做A X B

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1、 Ordered pair and Cartesian product;

1. Definition; The first element appears in each subset, and the second element only appears in one subset. In this way, the definition of ordered pairs is ensured. The order of the first and second elements is different, and the corresponding ordered pairs are different;

Here are different ordered pairs of the same two elements:

Ordered pair & lt; a , b > = { { a } , { a , b } } < a, b> = \ { \{ a \} , \{ a , b \} \}< a,b>= {{a},{a,b}}

Ordered pair & lt; b , a > = { { b } , { a , b } } < b, a> = \ { \{ b \} , \{ a , b \} \}< b,a>= {{B}, {a, B}} 2, Cartesian product

Let a and B be any two sets. If the first member of the ordered pair is the element of a and the second member is the element of B, all such ordered pair sets are called the Cartesian product or direct product of sets a and B, and are recorded as a x B

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