Half-open interval
A half-open interval is an interval which has either a maximum or a minimum element but not both.
If a half-open interval has a minimum but no maximum, then it is denoted by
, where
is the supremum, or
if no supremum exists. Alternatively,
is the set of all
such that
and
.
If a half-open interval has a maximum but no minimum, then it is denoted by
, where
is the infimum, or
if no infimum exists. Alternatively,
is the set of all
such that
and
.
Examples
is a half-open interval with a minimum but no maximum.
is a half-open interval with a maximum but no minimum.
, the set of nonnegative real numbers, is a half-open interval with no supremum.
, the set of nonpositive real numbers, is a half-open interval with no infimum.
See also
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