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Math Help - 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 \{a_n\} is monotonic if a_{i + 1}\geq a_i or a_{i + 1} \leq a_i for all 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 a_{i+1}=a_i

    {1 , 2, 3, 4, ...} is monotonic since 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 " a_{n+1}> a_n" or " a_{n+1}< a_n" from " a_{n+1}\ge a_n" or " a_{n+1}\le a_n".

    Other texts use "monotone" only for " a_{n+1}> a_n" or " a_{n+1}< a_n" and use "non-decreasing" for " a_{n+1}\ge a_n" and "non-increasing" for " a_{n+1}\le a_n".
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