# What Is A Monotonic Sequence?

• Apr 30th 2009, 03:50 PM
fattydq
What Is A Monotonic Sequence?
What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?
• Apr 30th 2009, 05:48 PM
Prove It
Quote:

Originally Posted by fattydq
What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?

A sequence $\displaystyle \{a_n\}$ is monotonic if $\displaystyle a_{i + 1}\geq a_i$ or $\displaystyle a_{i + 1} \leq a_i$ for all $\displaystyle i \geq 1$.
• Apr 30th 2009, 08:24 PM
chabmgph
Quote:

Originally Posted by fattydq
What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?

For example,

{1, 1, 1, 1, ...} is monotonic since $\displaystyle a_{i+1}=a_i$

{1 , 2, 3, 4, ...} is monotonic since $\displaystyle a_{i+1}>a_i$

{1, -1, 1, -1,...} is not monotonic since that does not satisfy the definition.
• May 1st 2009, 02:36 AM
simplependulum
I am wondering what is the difference between "sticky" and "monotonic" ?
• May 1st 2009, 04:46 AM
HallsofIvy
Quote:

Originally Posted by simplependulum
I am wondering what is the difference between "sticky" and "monotonic" ?

Then please define "sticky"! I have never seen that as a mathematics term.

By the way, some texts use the term "strictly monotone" to distinguish the case "$\displaystyle a_{n+1}> a_n$" or "$\displaystyle a_{n+1}< a_n$" from "$\displaystyle a_{n+1}\ge a_n$" or "$\displaystyle a_{n+1}\le a_n$".

Other texts use "monotone" only for "$\displaystyle a_{n+1}> a_n$" or "$\displaystyle a_{n+1}< a_n$" and use "non-decreasing" for "$\displaystyle a_{n+1}\ge a_n$" and "non-increasing" for "$\displaystyle a_{n+1}\le a_n$".