Definition:Strictly Decreasing/Sequence/Real Sequence

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Definition

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


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

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


Also known as

A strictly decreasing sequence is also referred to as strictly order-reversing.


Examples

Example: $\sequence {n^{-1} }$

The first few terms of the real sequence:

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

are:

$1, \dfrac 1 2, \dfrac 1 3, \dfrac 1 4, \dotsc$


$S$ is strictly decreasing.


Also see


Sources