By now you will have seen several definitions in lectures. Many of them will be written in the form
Definition. A blah is …
That is, the definition is displayed and the word being defined is in italics (or underlined if somebody is writing by hand). Sometimes, one doesn’t bother with the display, and simply says, during a discussion, “We define a blah to be …”
What is likely to have been emphasized less is that there are several different kinds of definition. In this post I’d like to enumerate some of them and give examples. It’s very much worth being aware, each time you meet a definition, what kind it is.