Difference between revisions of "Increasing sequence"
From Encyclopedia of Mathematics
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| − | A sequence of real numbers | + | {{TEX|done}} |
| + | A sequence of real numbers $x_n$ such that for all $n=1,2,\ldots,$ the inequality $x_n<x_{n+1}$ is satisfied. Such a sequence is sometimes called a strictly-increasing sequence, the term "increasing sequence" being reserved for sequences that for all $n$ merely satisfy the inequality $x_n\leq x_{n+1}$. 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 $+\infty$. | ||
Latest revision as of 16:28, 1 May 2014
A sequence of real numbers $x_n$ such that for all $n=1,2,\ldots,$ the inequality $x_n<x_{n+1}$ is satisfied. Such a sequence is sometimes called a strictly-increasing sequence, the term "increasing sequence" being reserved for sequences that for all $n$ merely satisfy the inequality $x_n\leq x_{n+1}$. 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 $+\infty$.
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=14839
Increasing sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Increasing_sequence&oldid=14839
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article