Feminism: I became the school idol of a female-dominated campus

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The cross, derived from the Latin crux, meaning "fork", was originally a cruel torture instrument for the execution of criminals, popular in ancient Rome, the Persian Empire, Carthage and other places, and was usually used to execute rebels and slaves. It later evolved into a symbol of the Christian faith, symbolizing the crucifixion and death of Jesus, the redemption of sinners, and the symbol of love and redemption. It began to appear in the Christian church in 431 A.D. and was erected on the top of the church in 586 A.D.

Function, a mathematical term. The definition is usually divided into traditional definition and modern definition, the essence of the two definitions of function is the same, but the starting point of the narrative concept is different, the traditional definition is from the point of view of motion change, while the modern definition is from the point of view of set and mapping. The modern definition of a function is given a set of numbers A, assuming that the element in it is x, and applying the corresponding rule f to the element x in A, denoted as f(x), to get another set of numbers B, assuming that the element in B is y, then the equivalence relationship between y and x can be expressed by y=f(x), and the concept of function contains three elements: the definition domain A, the value range B, and the corresponding law f. The core of this is the correspondence law f, which is the essential feature of functional relations. [1]

Functions, first translated by the Chinese Qing Dynasty mathematician Li Shanlan, from his book Algebra. The reason for this translation is that "where there is a variable in this variable, then this is a function of the other", that is, a function refers to the change of a quantity with the change of another quantity, or that one quantity contains another quantity.

First of all, it is important to understand that a function is a correspondence that occurs between sets. Then, it is necessary to understand that there is more than one functional relationship between A and B. Finally, it is important to understand the three elements of a function. The correspondence of functions is usually expressed analytically, but a large number of functional relationships cannot be expressed analytically, and can be expressed in images, tables, and other forms [2]. Concept: In a process of change, the amount of change is called a variable (in mathematics, the variable is x, and y changes with the change of the value of x), and some values do not change with the variable, we call them constants. Independent variable (function): A variable that is associated with a quantity, and any value of this quantity can find a fixed value in its quantity. Dependent variable (function): When the independent variable changes and the independent variable takes a unique value, the dependent variable (function) has and only a unique value corresponding to it. Function value: In a function where y is x, x determines a value, y determines a value, and when x takes a, y is determined as b, and b is called the function value of a[2]. Is the wave function in the quantum world a mathematical description or an entityTA says praise124 reading 10,000 mapping definitionsLet A and B be two non-empty sets, and if, according to some correspondence, for any element a in set A, there is a unique element b corresponding to it in set B, then such correspondence (including sets A, B, and the correspondence between set A and set B) is called the mapping of set A to set B, which is denoted as . where b is called the image of a under mapping f, denoted as: ; A is called B with respect to mapping F's preimage. The set of images of all the elements in set A is denoted as f(A). Then there is: the mappings defined between sets of non-empty numbers are called functions. (The independent variable of a function is a special primitive, and the dependent variable is a special image)[2] Geometric meaning: A function is related to inequalities and equations (elementary functions). Let the value of the function be equal to zero, and from a geometric point of view, the value of the corresponding independent variable is the abscissa of the intersection point of the image and the X-axis; From an algebraic point of view, the corresponding independent variable is the solution of the equation. In addition, by replacing the "=" in the expression of the function (except for functions without expressions) with "<" or ">", and then replacing the "Y" with other algebraic formulas, the function becomes an inequality and the range of independent variables can be found [2]. Set theory If the binary relation of X to Y has a unique for each , such that , then f is called a function of X to Y, denoted as: . , f is called an n-element function [2]. The set of input values for the element X is called the defined domain of f; The set of possible output values Y is called the range of f. The domain of a function is the set of actual output values obtained by mapping f to all elements in the defined domain. Note that it is incorrect to call the corresponding domain a value range, and the value range of a function is a subset of the corresponding domain of the function. In computer science, the data types of parameters and return values determine the defined and corresponding domains of the subroutine, respectively. Therefore, defining the domain and the corresponding domain is a mandatory constraint that is determined at the beginning of the function. On the other hand, the range is related to the actual implementation [2]. Categorical monographic, full, double, monographic, monographic, and monoluminous functions that map different variables to different values. i.e.: for all and , when there is . The range of the full emission function is its corresponding domain. That is, for any y in the corresponding domain of the map f, there is at least one x satisfying y=f(x). A double-shot function, which is both single and full shot. It is also called one-to-one correspondence. The bijective function is often used to show that the sets X and Y are equipotential, i.e., have the same cardinality. If a one-to-one correspondence can be established between two sets, then the two sets are said to be equipotential [2].

The image of the number f is a set of pairs of points on a plane

, where x is taken to define all the members of the domain. Function graphs can help to understand and prove some theorems.

If X and Y are both continuous lines, then the image of the function is very intuitive, note that there are two definitions of the binary relationship between the two sets X and Y: one is a triplet (X, Y, G), where G is the graph of the relationship; The second is to simply define it in terms of the diagram of the relationship. With the second definition, the function f is equal to its image [2].

The

Origin of Development History Functions

The word "function" used in Chinese mathematics books is a translation. When Li Shanlan, a mathematician in the Qing Dynasty, translated "function" into "function" when he translated the book "Algebra" (1859).

In ancient China, the word "letter" and the word "contain" are common, and both have the meaning of "contain". The definition given by Li Shanlan is: "Heaven is contained in the formula, which is a function of heaven." "In ancient China, the four characters heaven, earth, people, and things were used to represent four different unknowns or variables. The implication of this definition is: "Whenever a formula contains the variable x, then the formula is called a function of x." So "function" means that the formula contains variables. The exact definition of an equation we mean an equation with unknowns. However, in the early mathematical treatise "Nine Chapters of Arithmetic" in China, the term equation refers to a simultaneous one-dimensional equation containing multiple unknown quantities, that is, the so-called system of linear equations [2].

Early ConceptsIn

the seventeenth century, Galileo, in his book The Two New Sciences, almost entirely included the concept of functions or variable relations, expressing the relations of functions in the language of words and proportions. Around 1637, Descartes had noticed the dependence of one variable on another in his analytic geometry, but because he was not aware of the need to refine the concept of functions at that time, no one had clarified the general meaning of functions until Newton and Leibniz established calculus in the late 17th century, and most functions were studied as curves.

In 1673, Leibniz first used the word "function" to mean "power", and later he used the word to denote the relevant geometric quantities of points on curves, such as the abscissa, ordinate, tangent length, etc. At the same time, Newton used "flow" to represent the relationship between variables in his discussion of calculus [2].

In the eighteenth century

, in 1718, John Bernoulli defined the concept of function on the basis of the Leibniz function: "a quantity consisting of any form of any variable and constant." What he meant was that all formulas consisting of variables x and constants were called functions of x, and emphasized that functions should be represented by formulas.

In 1748, Euler defined a function in his Introduction to Infinite Analysis as: "The function of a variable is an analytic expression consisting of some numbers or constants of that variable and any way." He called John Bernoulli's definition of a function analytic function, and further distinguished it into algebraic and transcendental functions, and also considered "arbitrary functions". It is not difficult to see that Euler's definition of a function is more general and broader than that of John Bernoulli.

In 1755, Euler gave another definition: "If some variables depend in one way or another on others, i.e., when the latter variables change, the preceding variables also change, we call the preceding variables a function of the subsequent variables." [2]

In 1821, Cauchy gave a definition starting from the definition of variables: "There is a certain relationship between certain variables, and when the value of one of the variables is given, the value of the other variables can be determined, then the initial variable is called the independent variable, and the other variables are called functions." In Cauchy's definition, the term independent variable first appears, while it is pointed out that there is not necessarily an analytic expression for a function. However, he still thinks that functional relationships can be expressed in multiple analytic expressions, which is a big limitation.

In 1822, Fourier discovered that certain functions could be represented by curves, a single formula, or multiple formulas, thus ending the debate over whether the concept of functions should be represented by a single formula, and advancing the understanding of functions to a new level.

In 1837, Dirichlet broke through this limitation and considered that it

did not matter how the relationship between and was established, and he broadened the concept of function, stating: "For every definite value of x in a certain interval, y has a definite value, and y is called a function of x." This definition avoids the description of dependencies in function definitions and is accepted by all mathematicians in a clear way. This is often referred to as the classic function definition.

After Cantor's set theory occupied an important position in mathematics, Oswald de Vibron used the concepts of "set" and "correspondence" to give a modern definition of functions, and further concretized the correspondence, definition domain and value range of functions through the concept of sets, and broke the limit of "a variable is a number", which can be a number or other objects [2].

Modern ConceptsIn

1914, F. Hausdorff used the ambiguous concept "ordinal" to define functions in the "Compendium of Set Theory", which avoided the concepts of "variables" and "correspondence" with unclear meanings. Kuratowski's 1921 definition of "ordinal" with the concept of sets made Hausdorf's definition very rigorous.

In 1930, a new modern function was defined as "If there is always an element y determined by set N corresponding to any element x of set M, then a function is defined on set M, denoted as f." Element x is called the independent variable and element y is called the dependent variable" [2].

The traditional

definition of function definition

is general, in a process of change, false