Examples are a crucial aid to learning and understanding ideas, and an Examples section is to be found in most near-complete definition articles in subject wikis, as well as in some fact articles.
Goals of the examples section
The example section should provide the following:
- Extremes testing: These are the extreme examples of a definition or fact. For instance, an extreme example of a set might be the empty set or one-point set. An extreme example of a number might be 0 or 1. Extreme examples, even when they seem trivial and uninteresting, are important because they give a baseline understanding of the definition. Another goal of extremes is to clear misconceptions in an understanding of the definition. For instance, a person reading the definition of topospaces:Hausdorff space may naively assume that the empty space and the one-point space cannot qualify to be Hausdorff.
- Representative range: The examples section should provide a reasonably representative range of situations. One criterion for representativeness of examples of a collection of objects is that any statement true for every example is highly likely to be true for everything in the collection.
- Litmus test for defining criteria: Going through each example and justifying why it is a definition, should help a learner reinforce every aspect of the definition. A person who has read and understood every example should have acquired competence in checking the defining criteria in arbitrary situations.
- Non-examples: Non-examples are also often useful -- they provide a contrast with the examples and help reinforce what is special in the examples that is not true in the non-examples.