An increasing sequence, also called a nondecreasing sequence, is a sequence 
satisfying 
for every index 
. It is strictly increasing if 
for every index 
. Similarly, decreasing
and strictly decreasing sequences
use 
and 
,
respectively.
If every 
,
these conditions are equivalent to 
for an increasing sequence and 
for a strictly increasing sequence. The corresponding
ratio conditions for decreasing and strictly
decreasing sequences
are 
and 
,
respectively.
