defined

Defined is the past participle of the verb define and functions as an adjective and a verb in English. It denotes that something has been given a precise meaning, scope, or value by a definition. In technical writing, terms may be described as defined within a system to indicate that their meaning is established and used consistently, avoiding ambiguity or circularity in reasoning.

In mathematics and logic, definedness is a core concept. A function is defined on a domain if every input in that domain has a corresponding output. A function is well-defined when the value it produces depends solely on the input, not on how the input is represented. Problems arise if the same input can be represented in different ways and yields different outputs. Classic examples include divisions by zero or taking roots of negative numbers in real arithmetic, where the function is not defined at certain points or is not well-defined for some representations.

In programming and computer science, a symbol or variable is defined when it has an assigned value within a given scope. Code that uses an undefined variable may cause a runtime error or undefined behavior, depending on the language. Some languages provide mechanisms to test whether a macro or symbol is defined, such as conditional compilation checks, while others require explicit initialization before use.

Etymology and usage-wise, defined derives from Latin definire, meaning to set bounds or limits. In technical contexts, defining a term is a foundational act that clarifies meaning and enables precise reasoning. The opposite of defined is undefined or ill-defined, indicating missing, ambiguous, or inconsistent specification. Related concepts include definition, definable, and definitional.