it s not a trivial thing
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.
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2026-07-05 16:50
How to distinguish between non-trivial and trivial solutions?
In a system of linear equations, a trivial solution was a solution where all the unknown variables were zero, while a non-trivial solution was a solution where there was at least one non-zero solution. For example, for a linear equation AX = 0, if the coefficient matrix was simplified by the Gauss elimination method to obtain all zero rows, then the unknown variables of the equation could be taken as zero, which was the trivial solution. This meant that all variables in the equation were free variables and there were infinite solutions. If the non-zero rows were obtained after the reduction, there was at least one non-zero solution, which was a non-trivial solution. This meant that there were constraints in the equation and there was more than one solution. In matrix algebra, there were trivial and non-trivial solutions to the zero distribution problem. For example, in Riemann's hypothesis, the trivial solution was all negative even numbers, while the non-trivial solution was more difficult to solve.
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2026-01-19 09:11
A trivial mind map.
I'm not a fan of online novels. I'm a person who loves reading novels. I can't provide you with a mind map of the novel's trivial notes. If you have any other questions about the trivia, I will try my best to answer them.
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2024-09-23 01:45
Appreciation of a trivial work
A Small Matter was published in modern China in 1926. This article was about a young man who changed his life because of a small matter.
The protagonist of the story was a young man named Zhang Qing. He worked in a company and was responsible for organizing the company's documents and information. One day, he found that an important document in the company was missing. He immediately went to find the owner of the document, but found that the owner of the document had left the company and could not be found.
Zhang Qing felt very depressed and helpless. He began to reflect on his work and why the documents had disappeared. He realized that his job was only to organize information for the company, and this information was not his own. He was just carrying out the company's mission. He began to think about his own meaning and value. He believed that he should not only work for the company, but should pursue his own value and meaning.
This incident made Zhang Qing think deeply and realize that he should pursue his own interests and dreams instead of working just to survive. He decided to leave the company and start his own career to pursue his dream.
"A Small Matter" was a short story about a young man who changed his life because of a small matter. The story left a deep impression on people by emphasizing the importance of personal value and free will.
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2024-09-21 06:56
There is a non-trivial solution
In matrix algebra, if the value of the determinate is 0, then there is a non-trivial solution (non-zero solution); if the value of the determinate is not equal to 0, then there is only a trivial solution (X = 0). This concept was part of advanced mathematics. When solving boundary value problems, one might need to consider finding a value that made the problem have a non-trivial solution (non-zero solution).
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2026-07-09 07:55
The meaning of trivial things
" Trivial matters " referred to those complicated, trivial, small, and often messy matters. These things were usually scattered. A single thing seemed insignificant, but when many of these things gathered together, it would consume people's time and energy. For example, small quarrels between children in the family, the entanglement of whether children were short-sighted or not, and other family trifles. These things often involved the details of daily life.
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2026-03-12 13:28
The teacher's trivial memories
Teachers are the most important guides on our path of growth. Their words and deeds will accompany us for the rest of our lives. In my memory, there was a teacher who inspired me deeply. Her name was Teacher Li.
Miss Li is our English teacher. She has a lot of teaching experience. She pays attention to cultivating the students 'oral expression skills and often lets us practice oral English in class. She taught us how to use various language tools such as computers and mobile phones so that we could learn and communicate better. She is also very concerned about the mental health of students and often exchanges with us to help students solve various problems.
In addition to teaching, Teacher Li was also an excellent counselor. She was very concerned about the students 'learning and often communicated with them to understand their difficulties and problems. If she found any student had any problems, she would take the initiative to help and support them. Once I encountered difficulties in my studies, Mr. Li not only listened to me patiently, but also gave me a lot of valuable suggestions and guidance, which benefited me a lot.
Ms. Li is not only excellent in teaching, she is also an excellent person. She was very kind, passionate, and patient. She always cared about the growth and development of every student. Her charisma moved me deeply and motivated me to pursue higher goals.
In my memory, Teacher Li was an outstanding teacher. Her teachings and help have benefited me greatly, and her spirit will accompany me for the rest of my life. I will always remember her kindness and work hard to become a useful person to repay her love for me.
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2024-09-21 02:38
A novel as good as Trivial Progress
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2025-01-17 07:07
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.
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2026-07-01 15:43
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!
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2026-07-06 20:26
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