# Open Interval

Also found in: Dictionary, Thesaurus, Wikipedia.
Related to Open Interval: Open set

## open interval

[′ō·pən ′in·tər·vəl]
(mathematics)
An open interval of real numbers, denoted by (a,b), consists of all numbers strictly greater than a and strictly less than b.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Open Interval

the set of points between two given points. In other words, if a and b are the coordinates of the two given points, then the set of points having coordinates x such that axb is an open interval. An open interval does not contain its end points and is denoted by (a, b). In contrast, the closed interval [a, b] contains its end points and consists of the points having coordinates x such that a ≤ x ≤ b.

References in periodicals archive ?
The measure m(a, b) of an open interval (a, b) in R is the length b - a of this interval.
The state transition matrix for the homogeneous linear system (1.2) on the open interval J is the family of fundamental matrix solutions t [right arrow] [PHI](t, r) parametrized by r [member of] J such that [PHI](r, r) = I.
problem (1) admits at least three weak solutions in X and, moreover, for each h > 1, there exists an open interval
Yet again, any real number x in the open interval (a, b) satisfies [PI](x, g(i + 1), ..., g(i + n)) = [sigma].
i.e., of non-empty intervals of [R.sub.[greater than or equal to] 0] where: (i) [/.sub.0] ={0}; (ii) singular and open intervals alternate; (iii) succesive intervals [/.sub.j] and [/.sub.j+1] are adjacent for all j [greater than or equal to] 0, (iv) if infinite, the sequence of intervals is progressive, i.e., for every t[member of][R.sub.[greater than or equal to] 0], there exists [member of] N such that t[member of][/.sub.j].
It represents the open interval corresponding to the saturated zone of the sediments.
In particular, we say that the composition F(f(x)) exists and is equal to h on the open interval (a, b) if
Assume that the function f: I [subset] R [right arrow] R for an open interval I has a simple root [alpha] [member of].
Consider a 'smooth function' f in an open interval containing a point at x = [x.sub.0] below in Figure 1:
[GAMMA](s) exist the least value in open interval [1,2], and monotone decreasing at the left side of the point, at the right side of the point monotone increasing.
Let ube a strictly increasing three times continuously differentiate function defined in an open interval I.
The [3-observers.sup.*] in the Euclidean 3-space -[[SIGMA].sup.*] of the negative universe "observe" intrinsic Special Relativity ([phi]SR) and hence observe Special Relativity (SR) for intrinsic angles [phi][psi] in the open interval (-[pi]/2, [pi]/2) in Fig.

Site: Follow: Share:
Open / Close