Nichtleer

"Nichtleer" is a German adjective that translates to "non-empty" in English. It is primarily used in formal and technical contexts, particularly in mathematics, computer science, and linguistics, to describe a set, collection, or group that contains at least one element. The opposite of "nichtleer" is "leer," meaning "empty."

In set theory, a non-empty set is any set that is not the empty set. The empty set is denoted by {} or Ø and contains no elements. Therefore, any set containing even a single element is considered non-empty. This distinction is fundamental when discussing operations on sets, such as unions, intersections, and subsets, where the presence or absence of elements significantly alters the outcome.

In computer science, the concept of non-empty applies to various data structures. For instance, a non-empty list or array is one that has at least one item. Similarly, a non-empty string contains at least one character. Checking if a collection is non-empty is a common operation to avoid errors or unexpected behavior when processing data. For example, attempting to access an element in an empty list would typically result in an error.

Linguistics may also employ the term "nichtleer" when referring to linguistic units. A non-empty word, for example, would be a word that has a sound or written form, as opposed to silence or an unarticulated space. The precise application of "nichtleer" can vary depending on the specific subfield and its established terminology.