High Quality Content by WIKIPEDIA articles! In mathematics, well-definition is a mathematical or logical definition of a certain concept or object (a function, a property, a relation, etc.) which uses a set of base axioms in an entirely unambiguous way and satisfies the properties it is required to satisfy. Usually definitions are stated unambiguously, and it is clear they satisfy the required properties. Sometimes however, it is economical to state a definition in terms of an arbitrary choice; one then has to check that the definition is independent of that choice. On other occasions, the required properties might not all be obvious; one then has to verify them. These issues commonly arise in the definition of functions.