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十九世紀的數学已經把函數的概念从解析式子这个桎梏之中解放了出來(指实变函數),並且提出了“对应性”,这說明当時已初步具有了現代一般的函數概念,首先提出这个概念的,是俄罗斯數学家罗巴切夫斯基,1834年時,關於函數概念,他寫过下面的話:“这个一般的概念要求:若有一个數,它隨着x的每一个值而確定,又随着x而逐漸变化,那麼这个數就称为函數。函数的意义,可以用解析式子表達,也可以用条件來表達;我們可籍这式子或条件來試驗所有的數目而选擇適合的數目;最後,由相依關係可能找出,也可能找不出。”經过三年(在1837年)这个概念由列仁-吉瑞荷通过函數定义的形式表示出來,这函數定义一直保留到現在:“y是变量x在區間a≤x≤b上的函數,如果这个區間上每一个x值对应着一个確定的y值;至於这种对应關係是怎样確定
In the nineteenth century, mathematics had liberated the concept of functions from the paradox of the analytic subtype (referring to the real variable function), and proposed the “correspondence”. This shows that at the time, the concepts of modern and general functions had been preliminarily established. The first proposed concept was the Russian mathematician Robachevsky. In 1834, regarding the concept of functions, he wrote the following: “This general concept requires that if there is a number, it will follow every If a value is determined and gradually changes with x, then this number is called a function. The meaning of the function can be expressed in terms of an analytical expression or in a conditional expression; we can test all the conditions or conditions Choose the appropriate number for the number of; and finally, the dependencies may or may not be found.” After three years (in 1837) the concept is represented by the form of a function defined by Lenin Ghirich. , This function definition has been retained until now: ”y is a function of the variable x in the interval a ≤ x ≤ b, if each x value in this interval corresponds to a certain y value; as to how this correspondence is determined