The concept reflects the essential attribute of things, and things also reflect things with this essential attribute. The sum of the objects reflected by a concept is called the extension of this concept. The sum of the essential attributes of an object reflected by a concept is called the connotation of this concept. The connotation and extension of concepts describe concepts qualitatively and quantitatively, and each concept is the unity of its connotation and extension. The connotation of the concept strictly determines the extension of the concept, and conversely, the extension of the concept completely determines the connotation of the concept.

The extension and connotation of the concept is a subjective understanding of the objective. Because people's understanding of objective things is developing and changing, the extension and connotation of a concept will inevitably change, but it has its relative stability in the process of development and change. At the stage of determining the mathematical science system, the extension and connotation of each mathematical concept are certain and mutually certain.