What Is A Monotonic Sequence?

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April 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?
April 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 $\{a_n\}$ is monotonic if $a_{i + 1}\geq a_i$ or $a_{i + 1} \leq a_i$ for all $i \geq 1$ .
April 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 $a_{i+1}=a_i$

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

{1, -1, 1, -1,...} is not monotonic since that does not satisfy the definition.
(as Prove It had pointed out already)
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 " $a_{n+1}> a_n$ " or " $a_{n+1}< a_n$ " from " $a_{n+1}\ge a_n$ " or " $a_{n+1}\le a_n$ ".

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