Left-open right-open interval
Left-closed right-open interval
Left-infinite right-open interval
Left-closed right-closed interval
Left-infinite right-closed interval
Left-open right-closed interval
Left-closed right-infinite interval
Left-open right-infinite interval
If two half-open intervals are disjoint and the endpoint of one lies in the other, then it must be equal to the endpoint of the other.
If we remove a smaller interval from a larger, the result is nonempty