According to traditional logic, the connotation of a word is its meaning, that is, its concept, which reflects the unique attributes of things. For example, the connotation of "commodity" is "labor products produced for exchange"; The extension of a term is the kind of thing that a term refers to. For example, the extension of "person" is the kind that everyone has been making up through the ages. As one of the modern logic textbooks, the difference between connotation and extension was put forward for the first time. Although later logicians have different views on the rationality of this distinction, the terms "connotation" and "extension" have been used to this day.

The same is true of mathematics.

For example, a prime number is the concept of a prime number: "A natural number greater than 1 cannot be divisible by other natural numbers except 1 and itself, in other words, this number has no other factors except 1 and itself; Otherwise, it is called a composite number. " Extension is a class of all prime numbers.

Their relationship is that connotation determines extension, and extension conforms to the provisions of connotation.

That is, the concept determines the set of classes, and the properties of the elements of this set are consistent with the concept.