The role of the number axis:
1, the number axis can visually represent numbers, and the points on the horizontal number axis correspond to real numbers one by one, that is, each real number can be represented by a point on the number axis.
2. Compare the sizes of real numbers, with 0 as the center, and the number on the right is greater than the number on the left!
3. The imaginary number can also be represented by the vertical number axis perpendicular to the horizontal number axis and with the same origin, thus forming a complex plane with the horizontal number axis.
4. Two mutually perpendicular number axes with the same origin can form a plane rectangular coordinate system; Three mutually perpendicular number axes with the same origin can form a spatial rectangular coordinate system to determine the position of an object.
The number axis has the completeness of numbers, which can represent both rational and irrational numbers (collectively called real numbers) and imaginary numbers. At the same time, a coordinate system can be established to form a relatively strict digital system.
On the number axis, real numbers are divided into infinite cells, and each cell has a unique real number corresponding to it. On the number axis, positive numbers are on the right of 0 and negative numbers are on the left of 0. The unit length on the number axis can be any unit, and its decimal places can be integers, decimals or fractions.
The number axis is not only used to represent integers and rational numbers, but also other types of irrational numbers and real numbers. Through the number axis, we can intuitively understand the relative size and distance relationship between real numbers, so as to perform operations and solve problems better in mathematics.
At the same time, the number axis is also widely used in statistics, physics, economics and other fields to help people better understand and analyze practical problems. On the number axis, there is a one-to-one correspondence between numbers and their corresponding points. A point on the number axis can be represented by an ordered real number pair (x, a), where x is the position of the point on the number axis and a is the real number corresponding to the point.
The left side of the number axis is negative infinity, and the right side is positive infinity. The integer 0 is located in the center of the number axis and the midpoint of all positive numbers and their antonyms. The distance on the number axis can be expressed as an absolute value. For example, the distance from point X to point Y is |y-x|.
The number axis plays an important role in mathematics teaching, especially in algebra, geometry and calculus. In algebra, we can use the number axis to represent the set of real numbers and solve equations and inequalities.
In geometry, the number axis is used to represent line segments, vectors and coordinate systems. In calculus, the number axis is used to represent the domain of definition and value of functions, and also to understand the concepts of limit, derivative and integral.
By counting axes, we can understand the nature and relationship of real numbers more intuitively, and make the learning and application of mathematics more intuitive and simplified. Therefore, the number axis is an important graphic tool, which is very helpful for learning and understanding mathematical concepts.