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The definition and generalization of this concept are as follows:

Take the concept of fruit as an example, it is a relatively broad concept, including apples, bananas, oranges, grapes and other different fruits. If you want to describe a fruit more specifically, you can define the concept by adding connotation. For example, by increasing the connotation of red, the concept of red apple is limited to only containing red apples.

Conversely, if you want to describe a fruit more generally, you can generalize the concept by reducing the connotation. For example, by reducing the connotation of red and grapes, citrus fruits are defined as all citrus fruits including oranges, grapefruit and lemons.

In addition to the examples of fruits, the definition and generalization of concepts are also widely used in other fields. In medicine, pneumonia is a broad concept, including bacterial pneumonia, viral pneumonia, fungal pneumonia and many other different types of pneumonia. If you want to describe a kind of pneumonia more specifically, you can define the concept by adding connotation. For example, bacterial pneumonia is to limit the concept to include only pneumonia caused by bacterial infection by increasing the connotation of bacterial infection.

In marketing, mobile phone is a broad concept, including various brands, models and functions of mobile phones. If you want to describe one of the mobile phones in more detail, you can define the concept by adding connotation. For example, the concept of iPhone 13Pro Max is limited to this specific mobile phone by adding the connotations of Apple brand, 13Pro Max model and 6.7-inch screen.

The definition of concepts in mathematics has the characteristics of accuracy, hierarchy and correlation.

1. Accuracy: Mathematical concepts must have strict definitions and clear properties, and there can be no ambiguity or uncertainty. For example, in mathematics, a square must have four equal sides and four right angles, and there can be no other changes and uncertainties.

2. Hierarchy: Concepts in mathematics are often hierarchical structures from abstract to concrete and from general to special. For example, in geometry, point is the most basic concept, and then the concepts of line, surface and body are gradually introduced on the basis of point. Similarly, in algebra, number is the most basic concept, followed by integer, rational number, real number and other concepts, which are gradually introduced on the basis of number.

3. Relevance: Concepts in mathematics are often interrelated and interdependent. For example, in geometry, angle and line are two related concepts, and the size of angle is defined by the included angle of two intersecting lines; Similarly, in algebra, equation and solution are two related concepts, and the solution is the value of an unknown quantity that satisfies the conditions of the equation.