Undefined

Undefined describes a quantity or value that does not have a determined meaning within a given formal system or context. It commonly arises when an expression falls outside the domain of a function, or when an operation lacks a permissible result according to the rules in use. The designation is not a specific value; rather, it signals that no value can be assigned in that context.

In mathematics, undefined occurs when an expression cannot be assigned a value in the specified number system. Examples include division by zero (such as 1/0), the logarithm of non-positive numbers, and the real square root of negative numbers. A function is defined only on its domain, the set of inputs for which the expression yields a real (or complex) value.

In calculus and analysis, certain limits can lead to indeterminate forms like 0/0 or ∞/∞, which are not defined as particular numbers without further analysis. Some systems extend definitions to assign values in specific contexts, but standard arithmetic regards these as undefined.

In computing, undefined has particular significance. In some languages, undefined is a primitive value (as in JavaScript), distinct from null. In low‑level languages, using an uninitialized variable or performing operations outside defined behavior results in undefined behavior, meaning the language standard provides no guarantees about the outcome.

Outside mathematics and computing, undefined can describe terms without a fixed reference or parameters that have not been specified. In data and logic, undefined values indicate missing or unknown information, often distinguished from explicit null or not applicable values.