topwaarde

Topwaarde is a Dutch term used to denote the highest or maximum value observed within a specified domain, such as a data set, a measurement series, or a mathematical function. In formal contexts the terms maximum or hoogste waarde are common, but topwaarde is frequently used in everyday statistical reporting to describe the peak value. A key distinction is that topwaarde refers to an observed value, while a supremum or upper bound may exist without being attained.

In a finite data set, the topwaarde is simply the largest element. For example, in the data set [4, 9, 2, 9], the topwaarde is 9. If several elements share this maximum, the topwaarde remains that same value, even though multiple positions may reach it.

When the domain does not guarantee that an upper bound is attained, a topwaarde as an element may not exist, though an upper bound can still be present. For instance, the set (0, 1) has an upper bound of 1 but no topwaarde, while its supremum is 1. In such cases, the concept of the supremum (least upper bound) is more appropriate in mathematical description.

Applications of the topwaarde include summarizing performance in statistics, setting target values in quality control, and comparing results across time or categories. The term is mainly a practical, descriptive label rather than a formal mathematical designation; in rigorous contexts, maximum or supremum are typically used.

See also: maximum, supremum, upper bound, data range.