函数糊涂概念扩散何时了？

近日，国家教育部发文，要求全国高校组织力量建设一批世界水平本科微积分课程。

  上世纪30年代，法国布尔巴基数学学派给出了函数的序偶标准定义。

   反观国内本科微积分教材，关于函数“y=f（x）”的传统定义，千篇一律，糊里糊涂（… …），谈何世界一流水平？

      我们认为，建设世界水平一流高校本科数学课程，函数的序偶定义是必不可少的，也是回避不了的，“躲”不过去。

  请见本文附件：函数的序偶定义。

袁萌 陈启清  11月20日

附件：DEFINITION

    A real fimction of one variable is a set f of ordered pairs of real numbers such that for every real number a one of the following two things happens:

    (i) There is exactly one real number b for which the ordered pair (a, b) is a member of f. In this case we say that f(a) is defined and we write f(a) = b. The number b is called the value of f at a.

    (ii) There is no real number b for which the ordered pair (a, b) is a member of f. In this case we say that f(a) is undefined.

    Thus f(a) = b means that the ordered pair (a, b) is an element of f. Here is one way to visualize a function. Imagine a black box labeled f as in Figure 1.2.1.

    ich  

    函数的序偶定义

    袁萌 陈启清  11月20日

    附件：

    DEFINITION

    A real fimction of one variable is a set f of ordered pairs of real numbers such that for every real number a one of the following two things happens:

    (i) There is exactly one real number b for which the ordered pair (a, b) is a member of f. In this case we say that f(a) is defined and we write f(a) = b. The number b is called the value of f at a.

    (ii) There is no real number b for which the ordered pair (a, b) is a member of f. In this case we say that f(a) is undefined.

    Thus f(a) = b means that the ordered pair (a, b) is an element of f. Here is one way to visualize a function. Imagine a black box labeled f as in Figure 1.2.1.

    ich

函数的序偶定义

  近日，国家教育部发文，要求全国高校组织力量建设一批世界水平本科微积分课程。

    上世纪30年代，法国布尔巴基数学学派给出了函数的序偶标准定义。

袁萌 陈启清  11月20日

附件：DEFINITION

    A real fimction of one variable is a set f of ordered pairs of real numbers such that for every real number a one of the following two things happens:

    (i) There is exactly one real number b for which the ordered pair (a, b) is a member of f. In this case we say that f(a) is defined and we write f(a) = b. The number b is called the value of f at a.

    (ii) There is no real number b for which the ordered pair (a, b) is a member of f. In this case we say that f(a) is undefined.

    Thus f(a) = b means that the ordered pair (a, b) is an element of f. Here is one way to visualize a function. Imagine a black box labeled f as in Figure 1.2.1.

    ich  

    函数的序偶定义

    袁萌 陈启清  11月20日

    附件：

    DEFINITION

    A real fimction of one variable is a set f of ordered pairs of real numbers such that for every real number a one of the following two things happens:

    (i) There is exactly one real number b for which the ordered pair (a, b) is a member of f. In this case we say that f(a) is defined and we write f(a) = b. The number b is called the value of f at a.

    (ii) There is no real number b for which the ordered pair (a, b) is a member of f. In this case we say that f(a) is undefined.

    Thus f(a) = b means that the ordered pair (a, b) is an element of f. Here is one way to visualize a function. Imagine a black box labeled f as in Figure 1.2.1.

    ich