Integerordered

Integerordered is a term used in mathematics and computer science to describe a property of a structure where the primary ordering is aligned with integers or with integer-valued keys. In its broad sense, an integerordered collection is one whose elements can be arranged, indexed, or compared using integer steps or integer keys, typically with a total order.

In mathematics, an integerordered set might refer to a set equipped with a total order that is isomorphic to a subset of the integers, such as the natural numbers or the integers themselves. This interpretation emphasizes monotone relations and discrete steps, where the order between elements corresponds to their position along the integer line.

In programming and data structures, integerordered describes data that is kept in order according to integer keys. For example, an array or list that maintains elements in nondecreasing order of associated integer timestamps, or a map keyed by integers that supports range queries. The concept is useful for enabling predictable iteration, efficient indexing, and fast range operations.

Usage and variants: Some libraries or codebases use the term as a naming convention (for example, IntegerOrderedCollection) to signal that order is defined by integers. The term is not a standard formal definition in all mathematical texts and may vary by context, so interpretation depends on surrounding documentation.

Related concepts include total order, monotonicity, discrete order, indexing, and ordered maps. Examples illustrate practical applications in data alignment, event sequencing, and versioned data systems. See also order, total ordering, and integer sequences.