Definition of Open interval

1. Noun. An interval that does not include its endpoints.

Exact synonyms: Unbounded Interval
Generic synonyms: Interval
Antonyms: Closed Interval

Definition of Open interval

1. Noun. (mathematics) an interval in the real number line which does not contain its supremum and infimum. If specified by a pair of real numbers, then it consists of all the points on the real line whose values lie strictly between those two real numbers. ¹

¹ Source: wiktionary.com

Lexicographical Neighbors of Open Interval

open fire
open fireplace
open flap
open floor plan
open fracture
open frame
open goal
open half space
open half spaces
open head injury
open heart surgery
open hospital
open house
open houses
open interest
open interval (current term)
open jaw
open letter
open letters
open lung biopsy
open market
open markets
open marriages
open matte
open mic
open mind
open minds
open one's big mouth

Literary usage of Open interval

Below you will find example usage of this term as found in modern and/or classical literature:

1. Introduction to the Theory of Fourier's Series and Integrals by Horatio Scott Carslaw (1921)
"Eg f(x) = l|x is monotonic in the open interval (0, 1), but not bounded. At first one might be inclined to think that a function which is bounded and ..."

2. Proceedings of the London Mathematical Society by London Mathematical Society (1904)
"Uniform Convergence throughout an open interval or Set.—A series of functions of x is said to be " uniformly convergent throughout an open interval or an ..."

3. The Theory of Functions of a Real Variable and the Theory of Fourier's Series by Ernest William Hobson (1907)
"Such an open interval has been termed by Cantor a semi-continuum. Of the two essential properties of the arithmetic continuum, that of connexity, ..."

4. Topics in Statistical Dependence by Henry W. Block, Allan R. Sampson, Thomas H. Savits (1990)
"Then the rank R(x) does not determine whether x is in the open interval or at ... If x now decreases further to the open interval corresponding to the next ..."

5. Elementary Real Analysis by Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner (2000)
"7.10.7 Let / be convex on an open interval that contains the closed ... In each case / is defined on an open interval (a, b) containing the point XQ. ..."

6. Real Analysis by Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson (1997)
"Since a uniform limit of a sequence of functions that are nondecreasing on an open interval is also nondecreasing on that interval, A(I) is closed. ..."

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