In order to ensure that the numbers representing the "k"-combinations of } are less than those representing "k"-combinations not contained in }, the "k"-combinations must be ordered in such a way that their largest elements are compared first. The most natural ordering that has this property is lexicographic ordering of the "decreasing" sequence of their elements. So comparing the 5-combinations "C" = {0,3,4,6,9} and "C"' = {0,1,3,7,9}, one has that "C" comes before "C"', since they have the same largest part 9, but the next largest part 6 of "C" is less than the next largest part 7 of "C"'; the sequences compared lexicographically are (9,6,4,3,0) and (9,7,3,1,0). Another way to describe this ordering is view combinations as describing the "k" raised bits in the binary representation of a number, so that "C" = {"c"1...,"c""k"} describes the number