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Definition of Open interval
1. Noun. An interval that does not include its endpoints.
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
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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