Further conventions are also sometimes seen, including one based on relations. For a relation {{math|''R''}} on a set {{math|''S''}}, one may denote the set of objects related by ''R'' tolementto some element {{math|''x''}} of {{math|''S''}} by {{math|''S''<sub>''R''</sub>(x)}}. So from the notation | for the ''divides'' relation of [[number theory]], one may denote the set of factors of an integer {{math|''n''}} by {{math|'''Z'''<sub> | </sub>(''n'')}}. Similarly, a subset of {{math|''X''}} is a ''principal'' [[lower set]] of a poset {{math|(''X'', ≤)}} precisely if it can be denoted by {{math|''X''<sub>≤</sub>(''x'')}} for some {{math|''x''}} in {{math|''X''}}. And since {{math|~}} is the symbol for the [[adjacency relation]], the subset of a collection {{math|''W''}} of vertices of a [[graph (mathematics)|graph]] that includes exactly those adjacent to a vertex {{math|''v''}} (namely, the [[intersection (set theory)|intersection]] of {{math|''W''}} with the [[neighbourhood (graph theory)|open neighborhood]] of {{math|''v'')}} may be denoted by {{math|''W''<sub>~</sub>(''v'')}}.
