Ivan Shishkin, Birch Grove

Interval

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Revision 5052

9/15/2026, 5:50:38 PM · darktoaster

(-oo,3) is an open interval + link for open interval

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1An interval is a [[Subset|subset]] $I$ of the [[Real number|real numbers]] such that, for all $x<y\in I$, $xt+(1-t)y$ belongs to $I$ for all $t\in[0,1]$.
2Intuitively, $I$ contains every number between two given boundaries. It is hence a [[Convex set|convex set]].
3
4##### Examples and remarks
5- $[2,5]$ is the set of numbers between 2 and 5, including 2 and 5 (it is a [[Closed interval|closed interval]]).
5- $[2,5]$ is the set of numbers between $2$ and $5$, including $2$ and $5$ (it is a [[Closed interval|closed interval]]).
6- $(2,5)$ is the set of numbers between 2 and 5, excluding 2 and 5 (it is an [[open interval|open interval]]).
6- $(2,5)$ is the set of numbers between $2$ and $5$, excluding $2$ and $5$ (it is an [[intervalle-ouvert|open interval]]).
7- $(-\infty,3)$ is the set of numbers less than 3. It is not open, neither closed.
7- $(-\infty,3)$ is the set of numbers strictly less than $3$. It is an open interval.

Revision 5050

9/15/2026, 5:46:00 PM · darktoaster

Shared settings updated from fr translation

domainSet theoryReal analysis

Revision 928

8/5/2026, 7:18:25 AM · Sequoia

Concept edited

Compare with revision 8815 changed lines
1An interval is a [[Subset|subset]] of the [[Real number|real numbers]] containing every number between two given boundaries.
1An interval is a [[Subset|subset]] $I$ of the [[Real number|real numbers]] such that, for all $x<y\in I$, $xt+(1-t)y$ belongs to $I$ for all $t\in[0,1]$.
2Intuitively, $I$ contains every number between two given boundaries. It is hence a [[Convex set|convex set]].
2
3##### Examples and remarks
4- $[2,5]$ is the set of numbers between 2 and 5, including 2 and 5 (it is a [[Closed interval|closed interval]]).
5- $(2,5)$ is the set of numbers between 2 and 5, excluding 2 and 5 (it is an [[open interval|open interval]]).
6- $(-\infty,3]$ is the set of numbers less than or equal to 3.
7- $(-\infty,3)$ is the set of numbers less than 3. It is not open, neither closed.

Revision 881

8/3/2026, 7:29:58 PM · Ancient Tree

Concept marked usable

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Revision 880

8/3/2026, 7:29:52 PM · Ancient Tree

Concept created

Recorded titleInterval
Recorded typeDefinition
An interval is a [[Subset|subset]] of the [[Real number|real numbers]] containing every number between two given boundaries.

##### Examples and remarks
- $[2,5]$ is the set of numbers between 2 and 5, including 2 and 5 (it is a [[Closed interval|closed interval]]).
- $(2,5)$ is the set of numbers between 2 and 5, excluding 2 and 5 (it is an [[open interval|open interval]]).
- $(-\infty,3]$ is the set of numbers less than or equal to 3.