closed interval


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closed interval

n.
A set of numbers consisting of all the numbers between a pair of given numbers and including the endpoints.

closed interval

n
(Mathematics) maths an interval on the real line including its end points, as [0, 1], the set of reals between and including 0 and 1
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Noun1.closed interval - an interval that includes its endpoints
interval - a set containing all points (or all real numbers) between two given endpoints
open interval, unbounded interval - an interval that does not include its endpoints
References in periodicals archive ?
Let [GAMMA] = {[E.sub.1], [E.sub.2], ..., [E.sub.N]} be a [DELTA]-partition of compact set E satisfying the relations (4.7)-(4.9), [LAMBDA] = {0 = [w.sub.0], [w.sub.1], ..., [w.sub.a] = H} (a [less than or equal to] 1) be a uniform partition of the closed interval [0, H], where [w.sub.j] = j/a H and [delta] = H/a is the diameter of the partition [LAMBDA].
If [??], [??] are two soft real numbers with [mathematical expression not reproducible]; then [mathematical expression not reproducible] is said to be soft closed interval with boundary points [??] and [??].
A general closed interval [a, b] is identified by two real numbers a, b [member of] R and is defined as
Let E [subset or equal to] R be a closed interval. Define f : E [right arrow] E to be a continuous mapping.
The [alpha]-cut of the triangular fuzzy variable [??] = ([a.sub.l], a, [a.sub.u]) is the closed interval [[??].sub.[alpha]] = [[a.sub.l.sup.[alpha]], [a.sub.u.sup.[alpha]]] = [(a - [a.sub.l])[alpha] + [a.sub.l], -([a.sub.u] - a)[alpha] + [a.sub.u]], [alpha] [member of] (0, 1].
A d-interval I is a nonempty subset of [L.sub.1] [union] [??] [union] [L.sub.d] such that each component I [intersection] [L.sub.i] is either empty or a closed interval. The packing number of a set [Imaginary part] of d-intervals is the maximum number of pairwise disjoint elements of [Imaginary part], and this quantity is denoted [upsilon]([Imaginary part]).
We consider the problem of finding the roots of a given real-valued equation f (x) = 0 on a closed interval D = [a, b], which we write as a fixed-point equation x = g(x).
In the final section of the paper, we assert the notion of multiplicative Lipschitz condition on the closed interval [x, y] [subset] (0, m).
A set consisting of a closed interval of real numbers such that a [less than or equal to] x [less than or equal to] b is called an interval number.