Are strictly increasing/decreasing sequences considered monotone? A sequence which is either non-decreasing or non-increasing  is said to be monotone, this is the definition we have been given. But if a sequence is strictly increasing or strictly decreasing then that doesn't mean it is monotone so monotone is only if it is non-decreasing or non-increasing. Am I correct or not?
 A: Monotone in words means it can only increase or it can only decrease. And in that case for instance a strictly increasing sequence is monotone since it cannot decrease.
A: A sequence of real numbers $(s_n)$ is:


*

*monotone if $s_n \leq s_{n+1}$ for all $n \in \mathbb{N}$ or $s_n \geq s_{n+1}$ for all $n \in \mathbb{N}$.

*strictly increasing if $s_n < s_{n+1}$ for all $n \in \mathbb{N}$.

*strictly decreasing if $s_n > s_{n+1}$ for all $n \in \mathbb{N}$.


As $s_n < s_{n+1}$ for all $n \in \mathbb{N}$ implies $s_n \leq s_{n+1}$ for all $n \in \mathbb{N}$, a strictly increasing sequence is monotone.
As $s_n > s_{n+1}$ for all $n \in \mathbb{N}$ implies $s_n \geq s_{n+1}$ for all $n \in \mathbb{N}$, a strictly decreasing sequence is monotone.
In summary, strictly increasing and strictly decreasing sequences are monotone.
A: A sequence is monotone if it is either non-increasing or non-decreasing.
That is, $(s_n)$ is monotone if either $\forall n \in \mathbb{N}$, $s_{n+1} \geq s_n$ or $\forall n \in \mathbb{N}$, $s_{n+1} \leq s_n$
