noncreasing

Nondecreasing is a term used in mathematics to describe a sequence or function that does not decrease over time or across its domain. In other words, it is a sequence or function where each term or value is greater than or equal to the previous term or value. This concept is often contrasted with strictly increasing, where each term or value is strictly greater than the previous one.

For a sequence {a_n}, it is nondecreasing if for all n, a_n ≤ a_{n+1}. For a function f(x), it is nondecreasing if for all x1, x2 in the domain of f with x1 ≤ x2, f(x1) ≤ f(x2).

Nondecreasing functions are important in various areas of mathematics and its applications. They are used in optimization problems, where the goal is to find the maximum or minimum value of a function. They are also used in the study of limits and continuity, as well as in the analysis of algorithms and data structures.

In summary, nondecreasing is a fundamental concept in mathematics that describes sequences or functions that do not decrease over time or across their domain. It has wide-ranging applications in various areas of mathematics and its applications.