What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?
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 "$\displaystyle a_{n+1}\le a_n$".