First, they have opposite meanings and opposite symbols;
Second, they all represent a certain amount (the amount is not necessarily the same).
For example, the reservoir water level rising by 0.7 meters and falling by 0.4 meters are two quantities with opposite meanings. If an increase of 0.7 m is recorded as +0.7 m, a decrease of 0.4 m should be recorded as -0.4 m, and two numbers with equal absolute values and opposite signs are mutually opposite numbers. For example, -2 and +2 are opposite numbers. Obviously, the difference between the two concepts is not only that the former represents two quantities, but also that the latter represents two numbers.
Extended data:
The two basic classifications, quantity, amplitude and multiplicity (or number), contain significant differences between continuity and dispersion.
The quantity belonging to the second degree is discrete and can be decomposed into inseparable units, such as collective nouns: army, fleet, sheep, government, company, party, crowd, choir and number. The amplitude is continuous and can be decomposed all the time, including all non-collective noun: universe, matter, energy, liquid and matter.
Along with the analysis of its essence and classification, the problem of quantity involves many closely related topics, such as the relationship between amplitude and multiplicity, dimension, equation, proportion, measurement, unit of measurement, number and number system, number types and their relationships.
In this way, quantity is an attribute that exists in the range of amplitude and order. Mass, time, distance, heat and angle are all common examples of quantitative attributes. The two amplitudes of a continuous quantity can be expressed by a mutually proportional relationship, which is a real number.
Quantity is an attribute, which is represented by amplitude and repetition times. It is the basic category of things like quality, essence, change and relationship. The concept of quantity begins with share, that is, an entity that can carry quantity. As a basic vocabulary, quantity refers to any quantitative attribute or characteristic of things.
Some quantities are determined by their properties (such as numbers), and some quantities are used as descriptions of states (attributes, dimensions and characteristics), such as weight and lightness, length and short, width and narrow, big and small, and more and less.
In mathematics, vectors (also known as Euclidean vectors, geometric vectors and vectors) refer to quantities with magnitude and direction. It can be imagined as a line segment with an arrow. The arrow indicates the direction of the vector; Line segment length: indicates the size of the vector. Only the magnitude corresponds to the vector, and the quantity without direction is called quantity (called scalar in physics).
Vector notation: print letters (such as A, B, U, V) in bold, and add a small arrow "→" at the top of the letter when writing.
If the starting point (a) and the ending point (b) of the vector are given, the vector can be recorded as AB (and added to the top →). In the spatial cartesian coordinate system, vectors can also be expressed in pairs. For example, (2,3) in the Oxy plane is a vector.
In physics and engineering, geometric vectors are more often called vectors. Many physical quantities are vectors, such as the displacement of an object, the force exerted on it by a ball hitting a wall and so on. On the contrary, it is scalar, that is, a quantity with only size and no direction. Some definitions related to vectors are also closely related to physical concepts. For example, vector potential corresponds to potential energy in physics.
The concept of geometric vector is abstracted in linear algebra, and a more general concept of vector is obtained. Here, a vector is defined as an element of a vector space. It should be noted that these abstract vectors are not necessarily represented by number pairs, and the concepts of size and direction are not necessarily applicable. Therefore, it is necessary to distinguish the concept of "vector" in the text according to the context when reading on weekdays.
However, we can still find the basis of a vector space to set the coordinate system, and we can also define the norm and inner product on the vector space by choosing a suitable definition, which enables us to compare abstract vectors with specific geometric vectors.
References:
Baidu Encyclopedia-Quantity