Intervallieroja

Intervallieroja is the term used to describe the border points that bound a mathematical interval on the real line or in more general spaces. They determine the extent of the interval and influence whether endpoints are included or excluded in the set.

In interval notation, an interval is specified by two endpoints a and b with a ≤ b. The inclusion or exclusion of these endpoints yields different types of intervals: open intervals (a,b) exclude both endpoints; closed intervals [a,b] include both; half-open or half-closed intervals [a,b) include a but exclude b; and (a,b] exclude a but include b.

For unbounded intervals, borders can be infinite. Examples include (-∞, c) and (d, ∞), where one end extends without bound in the real line. In standard topology on the real line, the finite endpoints a and b are boundary points of the interval, while the interior is (a,b). If a = b, the interval reduces to the single point {a}, whose boundary is {a}.

Examples help illustrate the concept: the interval [0,1] has borders 0 and 1, both included; the interval (0,1) has the same borders but excludes them; the interval (-∞,3) has a finite border at 3 and an unbounded left side.

Applications of intervallieroja appear across mathematics and computing. They are central to defining limits, continuity, and integration, and they underpin topological notions of boundary. In programming and data processing, interval borders are used to specify ranges for indexing, searching, and filtering.

See also: interval, boundary, endpoint, open set, closed set.