A sequence or arbitrary ordered set or one-dimensional array of numbers, , is said to be in descending order if each . For example, the aliquot sequence of 259 is in descending order: 45, 33, 15, 9, 4, 3, 1, 0, 0, 0 ... The aliquot sequence starting at 60, however, is not in descending order: 108, 172, 136, 134, 70, 74, 40, 50, 43, 1, 0, 0, 0 ...

In a trivial sense, the sequence of values of the sign function multiplied by -1 is in descending order: ... 1, 1, 1, 0, -1, -1, -1... When each in the sequence, set or array, then it can be said to be in strictly descending order.