Closed interval
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A closed interval is an interval which has both a maximum and a minimum element. Closed intervals are denoted by where
is the minimum and
is the maximum. In the interval
,
is also the infimum (greatest lower bound) and
is also the supremum (least upper bound). Alternatively, a closed interval
is the set of all
such that
satisfies both of the inequalities
and
.
Every closed interval is a closed set.
Examples
, the set of real numbers nonstrictly between
and
, is a closed interval.
For any real number , the set
containing only
is a closed interval.
See also
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