<P> There are two distinct meanings in current mathematical usage for the notion of the domain of a partial function from X to Y, i.e. a function from a subset X' of X to Y . Most mathematicians, including recursion theorists, use the term "domain of f" for the set X' of all values x such that f (x) is defined . But some, particularly category theorists, consider the domain to be X, irrespective of whether f (x) exists for every x in X . </P> <P> In category theory one deals with morphisms instead of functions . Morphisms are arrows from one object to another . The domain of any morphism is the object from which an arrow starts . In this context, many set theoretic ideas about domains must be abandoned or at least formulated more abstractly . For example, the notion of restricting a morphism to a subset of its domain must be modified . See subobject for more . </P> <P> In real and complex analysis, a domain is an open connected subset of a real or complex vector space . </P> <P> In partial differential equations, a domain is an open connected subset of the Euclidean space R n (\ displaystyle \ mathbb (R) ^ (n)), where the problem is posed, i.e., where the unknown function (s) are defined . </P>

Can 0 be a domain of a function