Answer to Question #107342 in Math for Riya

Question

Explain the process of “generalization” in mathematics, using an example related to
understanding volume. Further, explain how this process differs from the process of
“Particularization”.

Answer 1

Given two related concepts A and B, A is a "generalization" of B, if and only if both of the following hold:

1) Every instance of concept B is also an instance of concept A.

2) There are instances of concept A which are not instances of concept B.

For example, measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume.

Specialization (or particularization) is opposite to generalization.

In specialization, a group of entities is divided into sub-groups based on their characteristics.

For example, the concept of volume is a particularization of the concept of measure.