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mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive...

In mathematics, the unit interval is the closed interval [0,1], that is, the set of all real numbers that are greater than or equal to 0 and less than...

graph theory, an interval graph is an undirected graph formed from a set of intervals on the real line, with a vertex for each interval and an edge between...

intervals are associated to geometrical segments of the line. Operations and functions on numbers correspond to geometric transformations of the line...

are no gaps (values from intervals of the real line). Because of this continuity assumption, continuous optimization allows the use of calculus techniques...

\mathbb {R} } be an interval on the real line. A function f : I → R {\displaystyle f:I\to \mathbb {R} } is said to be absolutely continuous on I {\displaystyle...

{\displaystyle A\cap B} is connected. For example, any closed interval on the real line is unicoherent, but a circle is not. If a unicoherent space is...

there exists a real number such that, for every pair of points on the graph of this function, the absolute value of the slope of the line connecting them...

real-root isolation of a polynomial consist of producing disjoint intervals of the real line, which contain each one (and only one) real root of the polynomial...

the majorization inequality, is a theorem in elementary algebra for convex and concave real-valued functions, defined on an interval of the real line...

convex function defined on an open interval of the real line. Such a function need not be differentiable at all points: For example, the absolute value function...

real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extension of the set of the real...

compact subset of the real line: absolutely continuous ⊆ uniformly continuous = {\displaystyle =} continuous and, for a compact interval, continuously differentiable...

domain interval of the size δ {\displaystyle \delta } are as close to each other as we want. In other words, for a uniformly continuous real function...

In mathematics, a partition of an interval [a, b] on the real line is a finite sequence x0, x1, x2, …, xn of real numbers such that a = x0 < x1 < x2 <...

mathematics, the lower limit topology or right half-open interval topology is a topology defined on R {\displaystyle \mathbb {R} } , the set of real numbers;...

nested intervals theorem, which are strictly weaker in that there are non Archimedean fields that are ordered and Cauchy complete. When the real numbers...

In mathematics, an open set is a generalization of an open interval in the real line. In a metric space (a set with a distance defined between every two...

Ordinal number topology Real line Split interval Overlapping interval topology Moore plane Sierpiński space Sorgenfrey line Sorgenfrey plane Space-filling...

intervals of the real line with an empty intersection. Let A be the interval whose left endpoint a is as large as possible, and let B be the interval...