Nonsortability

Nonsortability refers to the property of a collection or dataset that cannot be arranged or ordered according to a specific set of criteria. This is often due to inherent characteristics of the data itself or the absence of a defined ordering principle. For example, a collection of distinctly unique, unrelated items without any common attributes might be considered nonsortable. Similarly, data lacking a defined comparison operator, such as comparing a color to a sound, would also be nonsortable.

In computational contexts, nonsortability can arise when elements in a list do not have a transitive relationship. Transitivity means that if item A relates to item B, and item B relates to item C in the same way, then item A must also relate to item C. If this property is violated, a consistent sorting order cannot be established. This can lead to errors or undefined behavior in sorting algorithms. The concept is distinct from unsorted data, which simply means the data has not yet been sorted but is capable of being sorted. Nonsortable data, by its nature, resists any attempt at a meaningful linear ordering.