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In mathematics, distance is one of the most basic concepts in functional analysis. The distance space defined by it connects topological space with normed linear space and other spaces, and it is the first contact concept of learning functional analysis. Distance refers to the length of a straight line between any two points.

1, the quantitative relationship between human brain and physical objects

Mathematical concept Mathematical concept is a form of mathematical thinking that the human brain reflects the quantitative relationship of real objects and the essential characteristics of spatial form. In mathematics, judgment and reasoning, as general forms of thinking, are expressed in the form of theorems, rules and formulas, and mathematical concepts are their basis.

2. Correctly understand and flexibly use mathematical concepts.

Correctly understanding and flexibly using mathematical concepts is the premise of mastering basic mathematical knowledge and operational skills, and developing logical argumentation and spatial imagination. To understand and form a mathematical concept correctly, we must make clear the connotation of this mathematical concept, the qualitative characteristics of the object, its extension and the scope of the object's quantity.

3. Expose its essential characteristics

Generally speaking, mathematical concepts reveal their essential characteristics in the form of definitions. But before that, there is a stage of understanding through examples, exercises and oral descriptions. Many mathematical concepts need to be represented by mathematical symbols.

4. Mathematical symbols are a unique way to express mathematical concepts.

For example, dy represents the differential of function Y, and mathematical symbols are a unique way to express mathematical concepts, which plays a great role in students' understanding and forming mathematical concepts. It simplifies and clarifies the thinking process of students mastering mathematical concepts. The definitions of many mathematical concepts are expressed by mathematical symbols, thus enhancing the scientific nature.

Many mathematical concepts also need to be represented by graphics. Some mathematical concepts are graphics themselves, such as parallelogram, pyramid, hyperbola and so on. Some mathematical concepts can be represented by images.