 A subset "S" of R"n" is bounded with respect to the Euclidean distance if and only if it bounded as subset of R"n" with the product order.However, "S" may be bounded as subset of R"n" with the lexicographical order, but not with respect to the Euclidean distance.A class of ordinal numbers is said to be unbounded, or cofinal, when given any ordinal, there is always some element of the class greater than it.