Kontinuális

Kontinuális is a Hungarian adjective meaning "continuous." In general use, it describes something that has no gaps, breaks, or abrupt changes, and that changes gradually over time or space.

In mathematics, continuity is a precise notion applied to functions and mappings. A real-valued function f is continuous at a point a if small changes in the input around a lead to small changes in the output around f(a). Formally, for every epsilon > 0 there exists a delta > 0 such that |x − a| < delta implies |f(x) − f(a)| < epsilon. A function is continuous on a set if it is continuous at every point of that set. This concept extends to general topological spaces via the preimage of open sets being open. Continuous functions preserve limits, map connected sets to connected sets, and satisfy the intermediate value theorem: they attain every value between f(a) and f(b) on an interval [a,b]. If the domain is compact, continuity implies uniform continuity. Differentiability implies continuity, but a continuous function need not be differentiable.

In physics and engineering, continuous concepts describe processes or signals without discrete jumps, such as a continuous medium or a continuous-time signal, contrasting with discrete models. In signal processing, a continuous-time signal is defined for every instant in time, unlike discrete-time signals sampled at specific moments. In statistics, a continuous distribution has probability over intervals rather than at individual points. The term appears across disciplines to denote uninterrupted, smoothly varying phenomena.