Is a sequence of all the same numbers monotonic? I'm wondering based on the definition of monotonicity:


  A sequence where $a_n\geq a_{n+1}$ for all $n\in\mathbb{N}$ is monotonic. 


So given that the sequence $a_n = 3$ is all the same numbers and is neither increasing or decreasing, is it monotonic?
Yes, a constant sequence (a number repeated indefinitely) is inceed monotonic: it is both monotonic non-decreasing, and monotonic non-increasing.

Hence, one can require that a sequence be strictly monotonic increasing or strictly monotonic decreasing. Under such a restriction, a constant sequence is neither strictly increasing nor strictly decreasing monotonically.
yes, because constant sequence is both increasing and decreasing sequence. so that it is monotonic.