Decreasing

Definition

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

Difference between decreasing and nonincreasing

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 $5,4,3,2,1$ is decreasing as it satisfies the rule above. On the other hand, the sequence $5,4,4,2,1$ is not decreasing since $4 = 4$ .

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Decreasing

Definition

Difference between decreasing and nonincreasing

Example