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

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- Apr 30th 2009, 03:50 PMfattydqWhat 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 PMProve It
- Apr 30th 2009, 08:24 PMchabmgph
- May 1st 2009, 02:36 AMsimplependulum
I am wondering what is the difference between "sticky" and "monotonic" ?

- May 1st 2009, 04:46 AMHallsofIvy
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 "$\displaystyle a_{n+1}\le a_n$".