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Thread: What Is A Monotonic Sequence?

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    What Is A Monotonic Sequence?

    What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?
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    Quote Originally Posted by fattydq View Post
    What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?
    A sequence $\displaystyle \{a_n\}$ is monotonic if $\displaystyle a_{i + 1}\geq a_i$ or $\displaystyle a_{i + 1} \leq a_i$ for all $\displaystyle i \geq 1$.
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    Quote Originally Posted by fattydq View Post
    What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?
    For example,

    {1, 1, 1, 1, ...} is monotonic since $\displaystyle a_{i+1}=a_i$

    {1 , 2, 3, 4, ...} is monotonic since $\displaystyle a_{i+1}>a_i$

    {1, -1, 1, -1,...} is not monotonic since that does not satisfy the definition.
    (as Prove It had pointed out already)
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    I am wondering what is the difference between "sticky" and "monotonic" ?
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    Quote Originally Posted by simplependulum View Post
    I am wondering what is the difference between "sticky" and "monotonic" ?
    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 "$\displaystyle a_{n+1}\le a_n$".
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