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.