Definition:Increasing/Sequence/Real Sequence

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Definition

Let $\sequence {x_n}$ be a sequence in $\R$.


Then $\sequence {x_n}$ is increasing if and only if:

$\forall n \in \N: x_n \le x_{n + 1}$


Also known as

An increasing sequence is also known as an ascending sequence.

Some sources refer to an increasing sequence which is not strictly increasing as non-decreasing or monotone non-decreasing.


Some sources refer to an increasing sequence as a monotonic increasing sequence to distinguish it from a strictly increasing sequence.

That is, such that monotonic is being used to mean an increasing sequence in which consecutive terms may be equal.

$\mathsf{Pr} \infty \mathsf{fWiki}$ does not endorse this viewpoint.


Examples

Example: $\sequence 1$

The first few terms of the real sequence:

$S = \sequence 1_{n \mathop \ge 1}$

are:

$1, 1, 1, 1, \dotsc$


$S$ is both increasing and decreasing.


Also see


Sources

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