unstetig

Unstetig is an adjective in German meaning not continuous, i.e., having discontinuities or abrupt, non-smooth changes. The opposite term is stetig, which denotes continuity or steadiness. The word is used in mathematics as well as in the sciences and in everyday language to describe irregular or non-smooth behavior.

In mathematics, unstetig describes objects that fail to be continuous on a given domain. A function can be unstetig at a point if the limit does not match the function’s value there, or if the left and right limits differ. Common types of Unstetigkeit include Sprungstetigkeit (jump discontinuity) and more general forms where limits do not exist or are unbounded. The concept is closely tied to the study of limits and is contrasted with stetig functions, which have well-defined limits at all points of their domain.

Beyond pure mathematics, unstetig is also used to characterize signals, processes, or data sets that exhibit abrupt changes, irregular timing, or intermittent behavior. In such contexts, more everyday terms like unregelmäßig or diskontinuierlich may be used for precision, but unstetig remains a standard technical descriptor.

Related terms include Unstetigkeit (the noun form), Stetigkeit (continuity), and Diskontinuität (discontinuity). In mathematical and technical writing, unstetig files or functions are described with explicit reference to the nature and location of their discontinuities.