Alusvahemikus

Alusvahemikus is an Estonian mathematical term used to describe the base interval on the real number line that forms the domain of definition or the input range for a function, model, or data set. The concept identifies the set of input values for which an object is defined, intended to be used, or considered valid in analysis or computation.

The word combines alus (base) with vahemik (interval), and the term is commonly found in Estonian mathematical and applied science texts. The alusvahemikus can be a closed interval [a, b], an open interval (a, b), or another interval form that bounds the inputs. It helps distinguish the foundational domain from the output range or from larger ambient spaces.

Usage and examples: In numerical methods or interpolation, the alusvahemikus specifies the input domain over which a method is designed to perform reliably. For instance, a polynomial f(x) defined by f(x) = x^2 on the alusvahemikus [0, 5] is valid only for x within that interval. In data analysis, a model calibrated on measurements from 0 to 1 has an alusvahemikus of [0, 1], and applying it outside that range may be inappropriate.

Relation to other concepts: Alusvahemikus is related to, but not identical with, the domain of definition and the input interval. It is a practical term emphasizing the foundational interval used for analysis, plotting, or computation. See also: domain, interval, real number line, interpolation, piecewise function.