Komplemente

Komplemente is the plural form of Komplement in German and is used to describe elements that complete or fill out something in various fields. The term appears most often in mathematics, logic, linguistics, and computer science, where a complement refers to what lies outside or completes a given object.

In set theory, the complement of a subset A within a universal set U consists of all elements of U that are not in A. It is denoted as A^c or A′, and can also be written as U \ A. Important properties include A ∪ A^c = U and A ∩ A^c = ∅. Complements can be described relative to a chosen universe; choosing a different U yields a different complement.

In logic and probability, the complement of a proposition P is its negation ¬P. The probability of the complement of an event is 1 − P(event). De Morgan’s laws express how complements interact with unions and intersections: the complement of a union is the intersection of the complements, and the complement of an intersection is the union of the complements.

In linguistics, a complement is a syntactic element that completes the meaning of a word or phrase, such as a clause or a noun phrase required by a verb or adjective. For example, in German a clause like "dass es regnet" can function as a complement clause to "glauben" (to believe): "Ich glaube, dass es regnet."

In computer science, complements appear in numeral representations, such as the bitwise one's complement and the two's complement used for encoding signed integers.

Overall, Komplemente denotes plural instances of a complement across disciplines, each serving to complete or complete relation to a base element.