# 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?

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Yes, a constant sequence is monotone. – André Nicolas May 17 '13 at 16:25
Technically, this is called weakly monotone, meaning, that $\forall n\in \mathbb{N}, a_n\leq a_{n+1}$. – Noy Soffer May 17 '13 at 16:26

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.

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OP liked it too! =1 – Amzoti May 18 '13 at 0:56

Yes, every constant sequence is monotone, in fact simultaneously monotone non-decreasing and monotone non-increasing.

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yes, because constant sequence is both increasing and decreasing sequence. so that it is monotonic.

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