Editing Interval (mathematics) (section)

===Integer intervals===
When {{mvar|a}} and {{mvar|b}} are [[integer]]s, the notation ⟦''a, b''⟧, or {{closed-closed|''a'' .. ''b''}} or {{math|{''a'' .. ''b''}{{null}}}} or just {{math|''a'' .. ''b''}}, is sometimes used to indicate the interval of all ''integers'' between {{mvar|a}} and {{mvar|b}} included. The notation {{closed-closed|''a'' .. ''b''}} is used in some [[programming language]]s; in [[Pascal programming language|Pascal]], for example, it is used to formally define a subrange type, most frequently used to specify lower and upper bounds of valid [[Indexed family|indices]] of an [[Array data type|array]].

Another way to interpret integer intervals are as [[Set-builder_notation#Sets_defined_by_enumeration|sets defined by enumeration]], using [[ellipsis]] notation.

An integer interval that has a finite lower or upper endpoint always includes that endpoint. Therefore, the exclusion of endpoints can be explicitly denoted by writing {{math|''a'' .. ''b'' − 1}} ,  {{math|''a'' + 1 .. ''b''}} , or  {{math|''a'' + 1 .. ''b'' − 1}}.  Alternate-bracket notations like {{closed-open|''a'' .. ''b''}} or {{math|[''a'' .. ''b''[}} are rarely used for integer intervals.{{citation needed|date=February 2014}}