Nonincreasing

Definition

We say a sequence of real numbers $a_1,a_2,...,a_n$ is nonincreasing if for all $1 \le k \le n-1$ we have $a_k \ge a_{k+1}$ .

Difference between nonincreasing and decreasing

Decreasing - $5,4,3,1$

Nonincreasing - $5,4,4,2$

In a decreasing sequence we cannot have 2 same numbers, but in a nonincreasing sequence we can.

Example

For example, the sequence $5,4,3,3,1$ is nonincreasing as it satisfies the rule above. On the other hand, the sequence $5,3,4,2,1$ is not nonincreasing since $3 < 4$ .

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Nonincreasing

Definition

Difference between nonincreasing and decreasing

Example