Difference between revisions of "Half-open interval"
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Revision as of 15:09, 5 March 2022
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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