A mathematical object is well defined if there is full information, with no ambiguity or contradiction, to meet the specifications of being such an object. For example, a well-defined function needs a domain, codomain, and an assignment defined for each argument with an image in the codomain. A notion such as ‘the smallest positive real number’ is not well defined, as no such real number exists. Well-definedness particularly applies for functions of equivalence classes defined in terms of representatives; for example, squaring is well defined in modular arithmetic as if x ≡ y (mod n), then x² ≡ y² (mod n), but absolute value is not well defined.