2. The description method is as follows: A={x∈Z| 1≤x≤5} Here, the set method of A and the description method of.
A belongs to the same set.
3. Graphical method (Venn diagram): A method of representing a set with the interior of a closed curve.
A set is a whole composed of specific elements, and there are infinite sets in life. How to describe these sets is a common problem in mathematics. In fact, just as there are different ways to describe a thing in life, there are many different ways to describe a collection. There are several common ways to describe a set.
Natural language method: that is, using ordinary natural language to describe. This method is often used in people's daily communication. For example, the textbooks we distribute in the new semester include Chinese, mathematics, foreign languages and so on. This description method is the natural language method of application. The advantage is that it is easy to understand and communicate with non-professionals, but the disadvantage is that it is not accurate, rigorous and concise. Mathematics is a very rigorous subject, so this language is generally not used to describe the set in mathematics.
There are three common methods to describe sets in mathematics: enumeration method, description method and Wayne diagram method.
The enumeration method is relatively simple, as the name implies, that is, enumerating the elements in the collection one by one, and then enclosing them with the unique wrapping braces of the collection. Of course, some infinite sets can be expressed by ellipsis as long as the law is embodied. For example, the set of natural numbers is represented by {1, 2,3-}. The advantage of this representation of a set is that it clearly shows the elements and numbers contained in the set. Therefore, it has an important application in expressing sets, and students should really master it.
Description method is the abbreviation of set feature description method, which is an important method to describe sets, and it is also a difficult method to master. First of all, it also follows the writing rules of general sets, that is, it should contain other contents with braces. The internal form consists of two parts, separated by a vertical line, and the elements in this set are on the left of the vertical line. This is very important, we should strengthen our understanding. The most common variables are those used to represent the solutions of numbers, points, equations or inequalities. Everyone should pay special attention to their writing. The right side of the vertical line shows the characteristics of the elements in this set, so that this part determines the real scope of a set. Common expressions are natural language (rarely seen in mathematics), function forms, equations and inequality expressions. Of course, as mentioned above, there are many different forms to describe the same thing, and there are also different forms to express the same set when describing a set. We usually choose to express it in the most confident and popular way. But no matter what form it is, it is essential to know clearly what the elements in this set are.