Can you give an example in a formal definition? I would like to give an example in a formal definition. My concern is, by giving an example, I am implicitly demonstrating that the definition is not precise/clear enough.
Is it acceptable to give an example in a formal definition?
In the definition itself, no. It just should be that: A definition. You should add examples and/or motivations in the surrounding text, so your reader (a befuddled human being, not an automaton!) sees what is going on, and where you want to go.