Editing Unit interval (section)

{{Short description|Closed interval [0,1] on the real number line}}
{{For|the data transmission signaling interval|Unit interval (data transmission)}}

[[File:Unit-interval.svg|thumb|The unit interval as a [[subset]] of the [[real line]]]]

In [[mathematics]], the '''unit interval''' is the [[interval (mathematics)|closed interval]] {{closed-closed|0,1}}, that is, the [[Set (mathematics)|set]] of all [[real number]]s that are greater than or equal to 0 and less than or equal to 1.  It is often denoted ''{{math|I}}'' (capital letter <big>{{mono|I}}</big>). In addition to its role in [[real analysis]], the unit interval is used to study [[homotopy theory]] in the field of [[topology]].

In the literature, the term "unit interval" is sometimes applied to the other shapes that an interval from 0 to 1 could take: {{open-closed|0,1}}, {{closed-open|0,1}}, and {{open-open|0,1}}.  However, the notation ''{{math|I}}'' is most commonly reserved for the closed interval {{closed-closed|0,1}}.