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

Some sources refer to such a sequence as (monotone) non-decreasing.


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