Explanation of Non-trivial Function Dependence Noun
In a functional dependence relationship, when the attribute set Y in the relationship is not a sub-set of the attribute set X, there is a functional dependence X→Y. This kind of functional dependence is called non-trivial functional dependence. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
Explanation of Non-trivial Multivalue Dependence Noun
In the relationship model, if there is a multi-valued dependence X->->Y, when Z is not equal to the empty set (X->->Y here is the multi-valued dependence under the consideration of other attributes Z), then X->->Y is called a non-trivial multi-valued dependence. For example, in the relationship (course C, teacher T, reference book B), U = C+T+B,(C,T) determines a set of B, but this set of B has nothing to do with T. It is only determined by C, that is,(C, T)->->B. Since T is not an empty set,(C,T)->->B is a non-trivial multi-valued dependence. It could be seen that non-trivial multi-valued dependence was a case of multi-valued dependence, as opposed to ordinary multi-valued dependence. Moreover, functional dependence could be seen as a special case of multi-valued dependence. When the group in multi-valued dependence was composed of one value, it became a functional dependence. The Extraordinary Ordinary Life novel is equally exciting. Everyone is welcome to click and read it!
Explanation of Ordinary Function Dependence Noun
In a relation, let the relation be R(U), and X and Y be a set of attributes on U. If X contains Y, then there must be X→ Y, which is called trivial functional dependence. For example, in employee relationships, the employee number could always determine itself (recorded as "employee number → employee number"), and the attribute set composed of employee number and gender could always determine the employee number or gender attribute (can be recorded as "(employee number, gender) → employee number" and "(employee number, gender) → gender" respectively). These were all trivial functional dependence. Simply put, one attribute (or set of attributes) was completely dependent on another attribute (or set of attributes). This dependence was obvious and direct. 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!
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!
What is a non-trivial function?
In the database, a non-trivial function was a special function. Its output not only depended on the input parameters, but also depended on external environmental factors or hidden states. This was different from the functions in mathematics. Mathematical functions were usually determinative. The same input always had the same output, but non-trivial functions might have different output for the same input. For example, if a function task was to return the current date and time, it had no input parameters, and the output depended on the external environment (the current date and time). This was a non-trivial function. In mathematics, for the Riemann zeta function, the negative even numbers were ordinary zeros, while the non-ordinary zeros were complex numbers. There were infinitely many, and the real part was between 0 and 1. However, the concept of non-ordinary zeros in mathematics was different from the non-ordinary functions in the database. The main feature of non-trivial functions was that the output was not completely dependent on the input. Different from ordinary functions, it was more flexible when dealing with special situations in the database. It had a wide range of applications, such as obtaining the current date and time in the database, or implementing complex business logic (the result not only depends on the input parameters, but also depends on the hidden state such as some data in the database). It had the advantages of flexibility. 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!
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!