continuous

Continuous is an adjective describing something without interruption in time, space, or substance. In everyday language it denotes a seamless, unbroken progression.

In mathematics, continuity is a precise concept that characterizes how a function behaves as its input varies. A real-valued function f is continuous at a point x0 if, roughly speaking, small changes in x near x0 produce small changes in f(x). Formally, for every epsilon > 0 there exists delta > 0 such that |x − x0| < delta implies |f(x) − f(x0)| < epsilon. A function continuous on an interval has no jumps or holes there; many familiar functions, including polynomials and trigonometric functions, are continuous everywhere, while functions with a sudden jump, such as the Heaviside step, are not. In topology the notion is generalized: a function is continuous if the preimage of every open set is open, and uniform continuity strengthens the property across the entire domain.

Continuous data denotes quantities that can take an uncountable set of values along a continuum, such as height, time, or temperature, in contrast to discrete data, which take only distinct values like integers. In physics and engineering processes may be described as continuous when changes occur without discrete steps, supporting models based on differential equations and calculus.

In computing and software engineering, continuous is used in workflows such as continuous integration (CI) and continuous delivery (CD), which automate testing, integration, and deployment to enable rapid, reliable software updates. Continuous monitoring refers to ongoing observation of systems, while continuous manufacturing aims to produce goods with minimal interruption.