Similarly sorted

Two sequences are similarly sorted if they are either both rising or both falling.
For instance

$a_1 \geq a_2 \geq \cdots \geq a_n$

$b_1 \geq b_2 \geq \cdots \geq b_n$

are similarly sorted (they are both falling as the index value increases).

It has been suggested that this article or section be merged into Sequences. (Discuss)

In mathematics, a sequence is a list of objects (or events) which have been ordered in a sequential fashion; such that each member either comes before, or after, every other member. More formally, a sequence is a function with a domain equal to the set of positive integers.

A series is a sum of a sequence of terms. That is, a series is a list of numbers with addition operations between them.