Interval
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Revision 928
8/5/2026, 7:18:25 AM · Sequoia
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1
An interval is a [[Subset|subset]] of the [[Real number|real numbers]] containing every number between two given boundaries.1
An 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 $t\in[0,1]$.2
Intuitively, $I$ contains every number between two given boundaries. It is hence a [[Convex set|convex set]].2
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##### Examples and remarks4
- $[2,5]$ 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
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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.