Increasing sequence
From Encyclopedia of Mathematics
A sequence of real numbers 
such that for all 
the inequality 
is satisfied. Such a sequence is sometimes called a strictly-increasing sequence, the term "increasing sequence" being reserved for sequences that for all 
merely satisfy the inequality 
. Such sequences are also known as non-decreasing sequences. All non-decreasing sequences which are bounded from above have a finite limit, while all those not bounded from above have an infinite limit, equal to 
.
Comments
See also Decreasing sequence.
How to Cite This Entry:
Increasing sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Increasing_sequence&oldid=32101
Increasing sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Increasing_sequence&oldid=32101
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article