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?
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$\begingroup$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.
$\endgroup$ 1 $\begingroup$Yes, every constant sequence is monotone, in fact simultaneously monotone non-decreasing and monotone non-increasing.
$\endgroup$ $\begingroup$yes, because constant sequence is both increasing and decreasing sequence. so that it is monotonic.
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