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Meaning of "closed interval" in the English dictionary

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DICTIONARY
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PRONUNCIATION OF CLOSED INTERVAL

closed interval play
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GRAMMATICAL CATEGORY OF CLOSED INTERVAL

noun
adjective
verb
adverb
pronoun
preposition
conjunction
determiner
exclamation
Closed interval is a noun.
A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.

WHAT DOES CLOSED INTERVAL MEAN IN ENGLISH?

Interval (mathematics)

In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0 and 1, as well as all numbers between them. Other examples of intervals are the set of all real numbers, the set of all negative real numbers, and the empty set. Real intervals play an important role in the theory of integration, because they are the simplest sets whose "size" or "measure" or "length" is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure. Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff. Intervals are likewise defined on an arbitrary totally ordered set, such as integers or rational numbers. The notation of integer intervals is considered in the special section below.

Definition of closed interval in the English dictionary

The definition of closed interval in the dictionary is an interval on the real line including its end points, as, the set of reals between and including 0 and 1.

WORDS THAT BEGIN LIKE CLOSED INTERVAL

closed
closed book
closed chain
closed circuit
closed community
closed company
closed corporation
closed cycle
closed fracture
closed game
closed primary
closed scholarship
closed season
closed sentence
closed set
closed shop
closed source
closed-captioned
closed-circuit television
closed-circuit television camera

WORDS THAT END LIKE CLOSED INTERVAL

arval
class interval
conferval
confidence interval
contour interval
interval
larval
lunitidal interval
Nerval
orval
serval
subinterval

Synonyms and antonyms of closed interval in the English dictionary of synonyms

SYNONYMS

Translation of «closed interval» into 25 languages

TRANSLATOR
online translator

TRANSLATION OF CLOSED INTERVAL

Find out the translation of closed interval to 25 languages with our English multilingual translator.
The translations of closed interval from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «closed interval» in English.

Translator English - Chinese

闭区间
1,325 millions of speakers

Translator English - Spanish

intervalo cerrado
570 millions of speakers

English

closed interval
510 millions of speakers

Translator English - Hindi

बंद अंतराल
380 millions of speakers
ar

Translator English - Arabic

الفترة المغلقة
280 millions of speakers

Translator English - Russian

отрезок
278 millions of speakers

Translator English - Portuguese

intervalo fechado
270 millions of speakers

Translator English - Bengali

বন্ধ ব্যবধান
260 millions of speakers

Translator English - French

intervalle fermé
220 millions of speakers

Translator English - Malay

Selang tertutup
190 millions of speakers

Translator English - German

abgeschlossenen Intervall
180 millions of speakers

Translator English - Japanese

閉区間
130 millions of speakers

Translator English - Korean

폐쇄 구간
85 millions of speakers

Translator English - Javanese

Interval tertutup
85 millions of speakers
vi

Translator English - Vietnamese

khoảng thời gian đóng
80 millions of speakers

Translator English - Tamil

மூடிய இடைவெளி
75 millions of speakers

Translator English - Marathi

बंद मध्यांतर
75 millions of speakers

Translator English - Turkish

Kapalı aralık
70 millions of speakers

Translator English - Italian

intervallo chiuso
65 millions of speakers

Translator English - Polish

przedział zamknięty
50 millions of speakers

Translator English - Ukrainian

відрізок
40 millions of speakers

Translator English - Romanian

interval închis
30 millions of speakers
el

Translator English - Greek

κλειστό διάστημα
15 millions of speakers
af

Translator English - Afrikaans

geslote interval
14 millions of speakers
sv

Translator English - Swedish

slutet intervall
10 millions of speakers
no

Translator English - Norwegian

lukket intervall
5 millions of speakers

Trends of use of closed interval

TRENDS

TENDENCIES OF USE OF THE TERM «CLOSED INTERVAL»

The term «closed interval» is normally little used and occupies the 108.884 position in our list of most widely used terms in the English dictionary.
0
100%
FREQUENCY
Little used
49
/100
The map shown above gives the frequency of use of the term «closed interval» in the different countries.
Principal search tendencies and common uses of closed interval
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «closed interval».

FREQUENCY OF USE OF THE TERM «CLOSED INTERVAL» OVER TIME

The graph expresses the annual evolution of the frequency of use of the word «closed interval» during the past 500 years. Its implementation is based on analysing how often the term «closed interval» appears in digitalised printed sources in English between the year 1500 and the present day.

Examples of use in the English literature, quotes and news about closed interval

EXAMPLES

10 ENGLISH BOOKS RELATING TO «CLOSED INTERVAL»

Discover the use of closed interval in the following bibliographical selection. Books relating to closed interval and brief extracts from same to provide context of its use in English literature.
1
Essential Calculus with Applications
Remarkably enough, there is also much that can be deduced from the mere fact that a function is continuous in an interval, especially in a closed interval, as we now show. 3.31. The continuous image of a closed interval a. The properties of a  ...
Richard A. Silverman, 2013
2
Fixed Points
We shall now prove that both a closed interval and a square are compact. All convex polygons have the same property, as well as a disc, a circle, and a sphere. Let us start with two examples of noncompact sets. They are the real line R and its ...
I͡Uriĭ Alekseevich Shashkin
3
Mathematical Analysis I
Hence if a monotonic function has a point of discontinuity on the closed interval [a ,b], then the closed interval with endpoints /(a) and /(6) cannot be contained in the range of values of the function. D Theorem 5. (The inverse function theorem).
V. A. Zorich, 2004
4
The Way of Analysis
The set determined by the strict inequalities a < x < 6 (for a < 6) we will call an open interval, written (a, 6); while the set determined by the non-strict inequalities a < x < b we will call a closed interval, written [a, b]. For the open interval we will ...
Robert S. Strichartz, 2000
5
The Mathematics Dictionary
A closed interval is an interval that contains all of its end points. A closed interval with end points a and b often is denoted by [a, b], but sometimes by ]a, b[ or (a, b). Sometimes an interval of real numbers is defined as any set of real numbers ...
R.C. James, 1992
6
Applied Interval Analysis: With Examples in Parameter and ...
This book is about guaranteed numerical methods based on interval analysis for approximating sets, and about the application of these methods to vast classes of engineering problems.
Luc Jaulin, 2001
7
How To Learn Calculus Of One Variable
The absolute extreme values (or simply the absolute extrema) of a continuous function in a closed interval: There is a method to find out: The absolute extreme values (or simply the absolute extrema). i.e., the maximum and / minimum values  ...
J. D. Ghosh, 2004
8
New Foundations for Physical Geometry: The Theory of Linear ...
If the closed interval lies entirely in A or entirely in u, then this is immediate: >, U H is by construction a linear order on A and on u such that all the closed intervals in each are closed quasi—lines. If the closed interval is not contained entirely in ...
Tim Maudlin, 2014
9
New Foundations for Physical Geometry: The Theory of Linear ...
If the closed interval lies entirely in A or entirely in u, then this is immediate: >, U H is by construction a linear order on A and on u such that all the closed intervals in each are closed quasi—lines. If the closed interval is not contained entirely in ...
Tim Maudlin, 2014
10
Global Optimization Using Interval Analysis: Revised And ...
This chapter describes one such closed interval system. It is consistent with both the existing real interval system and with basic arithmetic operations (BAOs) on all possible operands including those that lead to indeterminate forms. Different ...
Eldon Hansen, G. William Walster, 2003

8 NEWS ITEMS WHICH INCLUDE THE TERM «CLOSED INTERVAL»

Find out what the national and international press are talking about and how the term closed interval is used in the context of the following news items.
1
Reggae music good for the classroom - UTech lecturer finds genre …
So if you look at open interval and closed interval, those are what are used to create the scale of the musical structure that we use," he said. «Jamaica Gleaner, Mar 15»
2
Slidecast: John Gustafson Explains Energy Efficient Unum Computing
... which side of zero you're on, the difference between an open interval and a closed interval, which is exactly what makes this example break. «insideHPC, Mar 15»
3
How to detect fraudulent activity in a cloud without invading users …
... packets in a closed interval, to perform a first classification," the researchers explained in a paper. "In case a fraudulent activity is suspected, ... «Help Net Security, Nov 14»
4
A mathematician would ask: Is a lane a closed interval or an open …
Is letting your wheel touch a lane boundary driving “entirely within a single lane”? It turns out there is deep disagreement among courts on this ... «Washington Post, Nov 14»
5
Polygamous foreign marriages under US law
... of Service · Ad Choices. Next Story. A mathematician would ask: Is a lane a closed interval or an open interval? Eugene Volokh · November 5 ... «Washington Post, Nov 14»
6
Data Compression with Arithmetic Encoding
(In all cases, this is strictly a half-closed interval, so the probability range for 'A' is actually >= 0 and < .01.) With this model, my encoder can ... «Dr. Dobb's, Nov 14»
7
Girl expresses her love to boyfriend through math equation
... means the giving is negative infinity, then the other side would ] (closed interval symbol, specifically referring to stop) positive infinite giving. «Shanghaiist, Jan 14»
8
Microsoft's other mogul
The lab cooked up some fascinating ideas, but none of the seven start-ups it spun off made any money, and Mr Allen closed Interval Research ... «The Economist, Sep 13»

REFERENCE
« EDUCALINGO. Closed interval [online]. Available <https://educalingo.com/en/dic-en/closed-interval>. Apr 2024 ».
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