A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
The lexical definition of a term, also known as the dictionary definition, is the definition closely matching the meaning of the term in common usage. As its other name implies, this is the sort of definition one is likely to find in the dictionary. A lexical definition is usually the type expected from a request for definition, and it is generally expected that such a definition will be stated as simply as possible in order to convey information to the widest audience.
A circular definition is a type of definition that uses the term(s) being defined as part of the description or assumes that the term(s) being described are already known. There are several kinds of circular definition, and several ways of characterising the term: pragmatic, lexicographic and linguistic. Circular definitions are related to Circular reasoning in that they both involve a self-referential approach. Circular definitions may be unhelpful if the audience must either already know the meaning of the key term, or if the term to be defined is used in the definition itself.
A theoretical definition defines a term in an academic discipline, functioning as a proposal to see a phenomenon in a certain way. A theoretical definition is a proposed way of thinking about potentially related events. Theoretical definitions contain built-in theories; they cannot be simply reduced to describing a set of observations. The definition may contain implicit inductions and deductive consequences that are part of the theory. A theoretical definition of a term can change, over time, based on the methods in the field that created it.
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is .
