Interpretation of words
"Guanzi·Seven Laws": "Rigid and soft, light and heavy, large and small, real and virtual, far and near, and how many are counted." Yin Zhizhang's note: "All these twelve things , You must count to know the number."
"Historical Records: Qin Shihuang Benji": "Since now, except for the posthumous law. I am the first emperor. The next generations are counted, and the second and third generations are counted. The legend is infinite." Zhang Shoujie Zhengyi: "﹝Numbers﹞ Colors dominate."
The "Old Miscellaneous Metaphor Sutra" is under the scroll: "Ananda White Buddha:'The disciples of the Buddha today have an Arhat, and it is past. Those who live and be here today cannot be counted.'"
Shen Congwen's "Congwen Autobiography: A Lesson in the Revolution of 1911": "One, two, three, and four count the number of dead corpses."< /p>
2, strategy and power.
"Three Kingdoms·Wu Zhi·Zhang Wen Biography": "Zhuge Liangda sees counting, he must know that God is concerned about Qu Shen's suitability."
Five Dynasties Qiji "Look" poem: "Pictures of Six Dynasties There are many wars, but Chen Gong’s count is wrong."
Zhang Binglin's "Proverbs on Reforms": "It is because of the old name that has no loss, but happiness and anger are used, and the power is natural; he has no power and no decision to change the law. If you don’t know how to count, it’s not enough to determine great work."
Count (count) is also called counting. One of the basic concepts of arithmetic. The process of indexing the number of things. When counting, one usually refers to each thing, counts one by one, and reads the numbers 1, 2, 3, 4, 5, etc. in the positive integer column, and corresponds to the pointed thing one-to-one. This kind of process Called count. The above method of counting things one by one is called counting one by one. If counting according to several groups, it is called group counting.
Include counts are usually used to calculate the number of days in the calendar. Usually, when counting 8 days from Sunday: Monday will be the "first day", Tuesday will be the "second day", and the next Monday will be the "eighth day". When counting implicitly, Sunday (the starting day) will be the "first day", and therefore the next Sunday will be the "eighth day". For example, two weeks in French are quinze jours (15 days). Similarly, in Greek (δεκαπενθήμερο) and Spanish (quincena), the number 15 is also used as the base. This habit is also applied to other calendars: in the Roman calendar, nons (nine) is eight days before ides; in the Gregorian calendar, Quinquagesima (the Sunday before Lent, meaning 50) is on Easter 49 days ago.
Counts sometimes include numbers other than 1. For example, when counting money or changes, or when "plus two counts" (2,4,6,8,10,12...) or "plus five counts" (5,10,15,20,15,. ..)Time.
Counting can also be used (mainly by children) to learn about number names and number systems. From the current archaeological evidence, it can be inferred that the history of human counting is at least 50,000 years, and the development of this led to the development of mathematical symbols and counting systems. Ancient cultures mainly used counting to record economic data such as liabilities and capital (ie accounting).
Classification and addition counting principle
To accomplish one thing, there are n types of methods. In the first type of method, there are different methods. There is a different method in the second type of method...There are different methods in the nth type of method, so there are a total of: a different method to accomplish this.
The principle of stepwise multiplication and counting
To complete one thing, you need to divide it into n steps. There are different ways to do the first step, and there are different ways to do the second step‥ ‥‥, there are different ways to do the nth step, so there are a total of different ways to accomplish this thing.
Classified addition counting and step-by-step multiplication counting are two basic thinking methods for dealing with counting problems. Generally, when faced with a complex counting problem, people often divide it into several simple counting problems through classification or step by step. On the basis of solving these simple problems, they can be integrated to obtain the answer to the original problem. It is a method of thinking that is often used in daily life. Through the decomposition of complex counting problems, the comprehensive problem can be resolved into a combination of single problems, and then the single problems can be broken down to achieve the effect of simplifying the complex and turning the difficult into easy.
Return to the basics and look at the two counting principles. They are actually the promotion of addition and multiplication that students have learned since elementary school. They are the theoretical basis for solving counting problems. Because of the basic status of the two counting principles, and they have great flexibility in applying them to solve problems. In fact, the status of the two counting principles needs to be strengthened.
Arrangement and combination are two special and important counting problems, and the basic ideas and tools to solve them are the two counting principles. The arrangement and combination are proposed from the perspective of simplifying calculations, and they are summarized by specific examples. Get the concept of permutation and combination; apply the principle of step-by-step multiplication and count to get the formula of the number of permutations; apply the principle of step-by-step counting and the formula of the number of permutations to derive the formula of the number of combinations. For permutation and combination, there are two basic ideas throughout. One is to find a simple counting method based on the characteristics and laws of a type of problem, just like multiplication as a simple operation of addition; the other is to pay attention to the application of two counting principles to think and solve problem.
The learning process of the binomial theorem is a typical process of applying two counting principles to solve problems. The basic idea is to "guess first and prove it later." The conjecture is not concluded by analyzing the formal characteristics of the expansions where n takes 1, 2, 3, 4, but directly applying the two counting principles to analyze the characteristics of the expansion terms. The two counting principles are almost a common sense. Such a simple and simple principle is easy to learn, easy to understand, understand, and easy to use, but to reach the state of being able to use it, a certain amount of applied training is required.
Like one (a), ten, hundred, thousand, ten thousand, hundred thousand... etc., it is called the counting unit of number. These counting units are arranged in a certain order, and the positions they occupy are called digits.
What we commonly use is the decimal notation method. The so-called "decimal system" means that the relationship between every two adjacent counting units is: a large unit is equal to ten small units, that is to say, the relationship between them The progress rate is "ten". The counting unit should consist of two major parts: an integer part and a decimal part, and arranged in the following order: ……Hundreds of billions, tens of billions, billions, billions, tens of millions, millions, one hundred thousand, ten thousand, thousand, one hundred, ten, one (1) One-tenth, one-hundredth, one-thousandth, ... there is no largest counting unit for the integer part, and no smallest counting unit for the decimal part. When writing a number, if there is a decimal part, use a decimal point (.) to separate the integer from the decimal.
Mathematics term, form.
A number is expressed in the form of, where 1≤|a|<10, and n represents an integer. This numbering method is called scientific notation. Numbers with very large numbers, generally we use scientific notation to express, such as 6230000000000; we can use it to express.
From a straight perspective, the decimal point after the 6 in the number 6.23 is moved to the right by 12 digits. If 6.23×10^12 is written as 6.23E12, it means that the decimal point after the 6 in the number 6.23 is moved to the right by 12 places. Significant digits start from the number on the left that is not 0.
For example: 890314000 reserves three significant digits as
839960000 reserves three significant digits as
0.00934593 reserves three significant digits as
Chinese counting method
When counting, Chinese people often use strokes to draw the character "Zheng". A character "Zheng" has five strokes, representing 5 and two " The word "positive" is 10, and so on. This counting method is simple and easy to understand and is very popular among Chinese people. It is said that this method was originally used by theater clerks to record "water card accounts".
At the end of the Qing Dynasty and the beginning of the Republic of China, the theater (tea garden) was an important entertainment place in people's daily life. There are many audiences in the theater every day. But at that time there was no such thing as tickets, the theater arranged the case to attract spectators at the entrance of the theater, and when five people were seated, the secretary wrote a "zheng" on the big water sign and marked the name of the case. . There is a table of Eight Immortals in front of the seats, and visitors can enjoy a cup of tea while watching the show. Later, the case will be responsible for counting and charging. It was accurate at the time of checkout.
This method was abandoned with the implementation of the ticket system in theaters, but as a concise, easy-to-understand, and convenient notation, it has always been popular among the people. Many Chinese still keep the habit of counting with the word "positive" when counting votes, counting their belongings, etc.