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descending order (Definition)

A sequence or arbitrary ordered set or one-dimensional array of numbers, $ a$, is said to be in descending order if each $ a_i \ge a_{i + 1}$. 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 $ a_i > a_{i + 1}$ in the sequence, set or array, then it can be said to be in strictly descending order.



"descending order" is owned by CompositeFan.
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See Also: ascending order

Also defines:  strictly descending order
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Cross-references: function, aliquot sequence, numbers, sequence
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This is version 2 of descending order, born on 2006-07-27, modified 2006-08-07.
Object id is 8179, canonical name is DescendingOrder.
Accessed 10522 times total.

Classification:
AMS MSC06A99 (Order, lattices, ordered algebraic structures :: Ordered sets :: Miscellaneous)

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