What does non-trivial functional dependence mean?
Let a relation be R(U), and X and Y be the sets of attributes U. If X→Y and X does not contain Y, then X→Y is called a non-trivial functional dependence. For example, in employee relations, the employee number function determines every other attribute (such as employee number determines salary), which is a non-trivial functional dependence. In addition, for example,"(employee number, name) → gender", although the employee number attribute may be enough to determine the gender, this situation is also a non-trivial functional dependence. It was different from ordinary functional dependence. Ordinary functional dependence was that if X contained Y, then X→Y must exist.(For example, the employee number could always be determined by the function itself, that is,"employee number → employee number", or the attribute set composed of employee number and gender could always determine the employee number or gender attribute, such as "(employee number, gender) → employee number" and "(employee number, gender) → gender".) Usually, the main topic was non-trivial functional dependence. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
Non-trivial functional dependence and trivial functional dependence
Let X and Y be the attributes of a relation, and X→Y. If Y is contained in X, then X→Y is called a trivial functional dependence. If Y is not contained in X, then X→Y is called a non-trivial functional dependence. The trivial functional dependence was automatically established because it was determined by the reflexive nature of the functional dependence. The functional dependence that was generally studied was mostly non-trivial functional dependence. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
Non-trivial functional dependence and complete functional dependence
Non-trivial functional dependence: In the Relational Model, if there is an attribute set X and an attribute set Y, and X→Y, but Y is not a sub-set of X, this functional dependence is called a non-trivial functional dependence. For example, in the relationship between students (student number, name, class, course, grade), student number → grade was a non-trivial functional dependence, because grades were not a sub-set of student number, and the student number could determine the attribute of grades. Complete functional dependence: In a relationship, if a non-main attribute data item depends on all keywords, it is called complete functional dependence. For example, in the relationship course selection (student number, course number, score), the score was completely dependent on the combination of the student number and course number. This was because the student number or course number alone could not determine the score. Only the combination of the two could determine the score. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
What are the non-trivial functional dependence?
Let a relation be R(U), and X and Y be the sets of attributes U. If X→Y and X does not contain Y, then X→Y is called a non-trivial functional dependence. For example,(student number, course number) → personal score was a non-trivial functional dependence. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
trivial functional dependence and partial functional dependence
Based on context alone 1. ** Ordinary Function Dependence ** - In a database, let R(U) be a relation pattern on a set of attributes U, and X and Y be a set of attributes U. If Y is a sub-set of X (that is, Y X), then X→Y is a trivial functional dependence. - For example, in the relationship mode of students (student number, name, gender),{student number, name}→{name} is a trivial functional dependence, because the name itself is a part of {student number, name}. Semantically speaking, trivial functional dependence represented an obviously established dependence relationship. This dependence relationship did not actually contain much meaningful new information, because it only indicated that the dependence of a set of attributes on its own set must exist. 2. ** Part of Function Dependence ** - Let (X,Y) be the property set of the relation pattern (R). If (X→Y) exists a proper set of (X ') such that (X'→Y), then (Y) is partially dependent on (X). - For example, in the Relational Mode course selection (student number, course number, grades, course name),{student number, course number}→{course name}, but in fact,{course number}→{course name}, which meant that the course name only depended on the student number and the course number in the course number, not the entire {student number, course number}, so the course name was partially dependent on {student number, course number}. Partial functional dependence may cause data redundancy-like problems. In the standardized design of a database, it is usually necessary to eliminate partial functional dependence to achieve a higher standard. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
trivial and nontrivial functional dependence
If in a functional dependence, the attributes in the right attribute set are all a sub-set of the left attribute set, this functional dependence is called a trivial functional dependence. Conversely, if at least one attribute in the right attribute set is not a sub-set of the left attribute set, it is called a non-trivial functional dependence. For example, in the relation pattern R(A,B,C), if A→A exists, it is a trivial functional dependence, because A on the right is a sub-set of A on the left; if A→B exists, it is a non-trivial functional dependence, because B is not a sub-set of A. The concept of functional dependence was very important in the field of database design. It was an important basis for operations such as the normalisation of the relationship model. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
An example of functional dependence
The following are some examples of functional dependence: 1. In student relationships, the student number determined the student's name, age, and department. It could be expressed as student number → (name, age, department). Since one student number corresponded to one student, once the student number was determined, the corresponding name, age, and faculty would also be determined. 2. In the course selection relationship, the student number and the course number could be added together to determine the results of a student's course, that is,(student number, course number)→ results. A single student number or course number could not determine the results. This was a complete functional dependence. 3. In describing the relationship between students, student number → name, student number → department. Because one student number corresponded to one and only one student, and one student studied in a certain department, when the value of the "student number" attribute was determined, the value of "name" and "department" was also uniquely determined. 4. In the relationship mode, the course number determines the course name, which can be expressed as: course number → course name. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
Completely nontrivial functional dependence
In a functional dependence, let R(U) be the relation pattern on the property set U, and X and Y be a set of U. If X→Y (Y depends on X), and Y is not a sub-set of X (this is a non-trivial functional dependence), and for any proper sub-set X'of X, X' cannot determine Y (that is, the property of complete functional dependence), then Y is said to be completely non-trivial functional dependence on X. For example, in a relationship model (student number, course number) → grade, grade depends non-trivial on (student number, course number), and neither student number nor course number alone can determine grade. This is a completely non-trivial functional dependence. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
A detailed explanation of functional dependence
A functional dependence was a term derived from mathematics. When a set of attributes determined another set of attributes, the other set of attributes depended on the set of attributes. It represents the dependence of the value of one attribute or set of attributes on the value of another attribute or set of attributes. This dependence is the semantical property of the information expressed by the relationship itself, and cannot be determined by the way the attributes form the relationship, nor can it be determined by the current content of the relationship. For example, in a complete functional dependence, if a non-main attribute data item depended on all keywords in a relationship, it was called a complete functional dependence. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
How to understand partial functional dependence
Let X and Y be the two sets of attributes of relation R. If X→Y exists, and when X 'is a true set of X, X' →Y exists, then Y is said to be partially dependent on X. Simply put, Y could be obtained by depending on X, but Y was not completely dependent on X. There was a proper set of X that could also be obtained by Y. This situation was partial functional dependence. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
What does non-trivial function mean?
In mathematics, non-trivial functions were different from functions that were commonly understood. In the field of database, a non-trivial function was a special function. Its output not only depended on the input parameters, but also on some external environmental factors or hidden states. This led to the fact that for the same input, non-trivial functions might have different outcomes. For example, if a function is used to return the current date and time, the function has no input parameters, and its output depends on the external environment (the current date and time), this is a non-trivial function. In the mathematical concepts related to complex functions, such as the Riemann zeta function, there was the concept of the non-trivial zero point of the Riemann zeta function. However, the non-trivial zero point here was not a definition of the non-trivial function, but a definition of the special point where the value of the Riemann zeta function was zero. These points were important for studying the distribution law of prime numbers. In C, it was mentioned that non-trivial functions should have a Doxygen style function header. This was mainly from the perspective of programming specifications to ensure that the function header provided enough information to facilitate the use of the function and verification. It was not a definition of the nature of non-trivial functions. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!