In mathematics textbooks, q is a set of rational numbers, r is a set of real numbers, and RQ represents the remainder of the set of rational numbers in the set of real numbers. Irrational number is an infinite cycle decimal, which cannot be written as a real number of the ratio of two integers. All decimals and integers are real numbers. A set is an unordered sequence of non-repeating elements.
Set is a very practical language for us in our high school math textbooks. The related knowledge of set has a very important connection with other mathematical contents, so studying hard, mastering and using mathematical set skillfully plays the most basic role in the whole high school study. Set is a concept in mathematics textbooks. Simply put, many numbers are put together to form a set.
R: set of real numbers (including rational numbers and irrational numbers); Z: integer set {…,-1, 0, 1, …}; N represents a non-negative integer set; Q stands for rational number set. The set of all real numbers can be called real number system or real number continuum. Any complete Archimedean ordered field can be called a real number system.
The set of rational numbers, that is, the set of all rational numbers, is represented by the English letter Q in mathematics. Rational number set refers to a subset of real number set. Rational numbers can be divided into three categories: positive numbers, negative numbers and zero. Zero is the dividing line between positive and negative numbers; those greater than zero are positive numbers and those less than zero are negative numbers.
Problems needing attention in mastering set knowledge and set thought in an all-round way
1. Understand special conceptual elements: a set is determined by elements. The representation, classification and operation of sets are also characterized by elements. So although there are many concepts and relationships in the set, as long as we grasp the core concept of element, the set problem will be solved.
2. Grasp the special nature of mutual differences: When solving the problem of set elements, we must pay attention to the fact that the elements in the set should satisfy mutual differences to avoid root growth.
3. Pay attention to the special set empty set: an empty set is a set without any elements. We stipulate that an empty set is a subset of any set and a proper subset of any non-empty set. Therefore, when it comes to the relationship between sets, we should pay special attention to empty sets.
4. Using Wayne diagram, number axis and other special tools: the representation methods of sets can be divided into enumeration method, description method and graphic method. Enumeration generally represents a finite set, and description generally represents an infinite set, which is used to write the final result. In the process of operation, the number axis is generally used to represent the set of continuous elements, and the Wayne diagram is used to represent the set of discrete elements. Graphic language can help us find the answer quickly and intuitively, and improve the speed of solving problems.