First, the function introduction
Function, a mathematical term. Its definition is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.
The modern definition of a function is to give a number set A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another number set B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x). The concept of function includes three elements: domain A, domain B and corresponding rule F, the core of which is corresponding rule F, which is the essential feature of function relationship.
Second, the independent and dependent variables of the function
Independent variable (function): a variable related to other quantities, and any value in this quantity can find a corresponding fixed value in other quantities. Dependent variable (function): it changes with the change of independent variable. When the independent variable takes a unique value, the dependent variable (function) has and only has a unique value corresponding to it.
The origin and early concept of function;
1, the origin of the function
The word "function" used in China's math book is translated. It was Li, an algebra expert in China's Qing Dynasty, who translated "function" into "function" when he translated Algebra (1859). In ancient China, the word "Xin" and the word "Han" were universal and both had the meaning of "Han". Li's definition is: "every formula contains heaven, which is a function of heaven."
In ancient China, four different unknowns or variables were represented by four words: heaven, earth, people and things. The meaning of this definition is: "Whenever a formula contains a variable X, the formula is called a function of X", so "function" means that the formula contains a variable. The exact definition of an equation refers to an equation containing unknowns.
2. Early concepts
/kloc-in the 0/7th century, Galileo almost completely contained the concept of the relationship between functions or variables in his book Two New Sciences, and expressed the relationship between functions in words and proportional languages. Descartes noticed the dependence of one variable on another in analytic geometry around 1637, but he didn't realize that he wanted to refine the concept of function.