Area Mathematics - Functions / General concepts

IEV ref 103-01-12

en
interval
set of real numbers such that, for any pair (x, y) of elements of the set, any real number z between x and y belongs to the set

Note 1 to entry: There are several kinds of intervals:

• closed interval from a to b: $\left[a,\text{\hspace{0.17em}}b\right]=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a\le x\le b\right\}$
• open interval from a to b: $\right]a,\text{\hspace{0.17em}}b\left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a
• half-open intervals: $\right]a,\text{\hspace{0.17em}}b\right]=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a and $\left[a,\text{\hspace{0.17em}}b\left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a\le x
• closed unbounded interval up to b or onward from a: $\right]-\infty ,\text{\hspace{0.17em}}b\right]=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}x\le b\right\}$ and $\left[a,\text{\hspace{0.17em}}+\infty \left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a\le x\right\}$
• open unbounded interval up to b or onward from a: $\right]-\infty ,\text{\hspace{0.17em}}b\left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}x and $\right]a,\text{\hspace{0.17em}}+\infty \left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a

fr
intervalle, m
ensemble de nombres réels tel que, quel que soit le couple (x, y) d'éléments de l'ensemble, tout nombre réel z compris entre x et y appartient à l'ensemble

Note 1 à l'article: On distingue plusieurs catégories d'intervalles:

• intervalle fermé de a à b: $\left[a,\text{\hspace{0.17em}}b\right]=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a\le x\le b\right\}$
• intervalle ouvert de a à b: $\right]a,\text{\hspace{0.17em}}b\left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a
• intervalles semi-ouverts: $\right]a,\text{\hspace{0.17em}}b\right]=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a et $\left[a,\text{\hspace{0.17em}}b\left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a\le x
• intervalle illimité fermé commençant en a ou finissant en b: $\right]-\infty ,\text{\hspace{0.17em}}b\right]=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}x\le b\right\}$ et $\left[a,\text{\hspace{0.17em}}+\infty \left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a\le x\right\}$
• intervalle illimité ouvert commençant en a ou finissant en b: $\right]-\infty ,\text{\hspace{0.17em}}b\left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}x et $\right]a,\text{\hspace{0.17em}}+\infty \left[=\left\{x\in R\text{\hspace{0.17em}}|\text{\hspace{0.17em}}a

ar
فترة

cs
interval

de
Intervall, n

es
Intervalo

it
intervallo

ko
구간

ja

 nl be interval, n

pl
przedział
interwał (stosowany w akustyce)

pt
intervalo

sr
интервал, м јд

sv
intervall

zh