The present paper discusses set operations of half-open intervals (left-closed and right-open interval) as a mathematical approach to discrete representation of time ranges of species. At first, formulas are presented for set operations (union, intersection and complement) of half-open intervals included in a half-open interval T. Let T be an infinite set whose elements are an empty set, single intervals and unions of intervals. Then T is closed under set operations. Let SO be a set of species forming a higher rank of taxon Σ which lived in the true range T in time. Then the time ranges of species are elements of T and produce new elements of T consistently through set operations. The time range T is subdivided into a finite number of short time intervals at the appearance times and the extinction times of species in SO. The time range of species can be expressed in a form of union of the short time intervals. In the same manner as a set T, a finite set TM whose elements are an empty set, the short time intervals and unions of the short time intervals is closed under set operations. Finally, it is concluded that set operations of time ranges of species can be performed consistently as discrete processing of the short time intervals.