Question 2: What is the function of the number axis?

In mathematics, numbers can be represented by points on a straight line, which is called a number line, and it satisfies the following conditions: (1) Take any point on the line to represent 0, and this point is called the origin; (2) Generally, from the origin to the right (or upward) is the positive direction, and from the origin to the left (or downward) is the negative direction; (3) Choose an appropriate length as the unit length, and take a point every other unit length on the straight line from the origin to the right, indicating 1 (1 unit length to the right), 2 (2 unit lengths to the right), 3 (3 unit lengths to the right), …; From the origin to the left,-1 (left 1 unit length), -2 (2 unit lengths to the left) and -3 (3 unit lengths to the left) are expressed in a similar way.

Schematic diagram of number axis:

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.

5. 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.

Question 3: What is the one-to-one correspondence between points on the number axis? Real numbers acting on the number axis correspond to points on the number axis one by one, that is, each real number can be represented by a point on the number axis; On the contrary, every point on the number axis represents a real number.

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.

5. 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.