DOMAINs

In mathematics, a domain of a function or relation is the set of input values for which the function is defined. If a function f maps from a domain A to a codomain B, A is called the domain. The codomain is B. The domain determines where the formula can be evaluated without undefined operations. The domain may be distinct from the range of outputs the function actually produces.

Common examples include the domain of sqrt(x) being x ≥ 0; the domain of 1/x being x ≠ 0; and the domain of log(x) being x > 0. For functions of several variables the domain is a subset of R^n defined by constraints such as x > 0 and y ≥ 2. The domain may be restricted to ensure properties such as continuity or differentiability.

In computing, a domain also refers to a domain name in the Domain Name System. A domain is a hierarchical naming space used to identify resources on the Internet. Domain names are read from right to left and commonly end with a top-level domain such as .com or .org, or a country code. DNS translates names to IP addresses and supports a range of records (A, CNAME, MX, TXT) used to route traffic and verify identity.

Beyond mathematics and networking, domain can denote an area or context of activity, knowledge, or influence. In logic, the domain of discourse is the set of objects under consideration. In problem solving, the domain defines where rules apply and which values are admissible.