DreierTupel

DreierTupel, also known as a "triple" or "ordered triple," is a fundamental concept in mathematics and computer science, representing a sequence of three elements. It is commonly used to denote ordered sets where the sequence and distinctness of elements matter. The term originates from the German word "Dreier," meaning "three," and "Tupel," which translates to "tuple."

In mathematics, a triple is often used to represent points in three-dimensional space, where each element corresponds to a coordinate along an axis. For example, the triple (x, y, z) specifies a unique location in 3D Cartesian coordinates. This notation is widely applied in geometry, physics, and engineering to describe spatial relationships.

In computer science, triples are frequently employed in data structures such as tuples, which are immutable sequences of elements. They are particularly useful in functional programming languages, where tuples allow the grouping of heterogeneous data types without the overhead of creating custom objects. For instance, a tuple like (name, age, score) can store related but distinct pieces of information compactly.

Triples also play a role in formal logic and knowledge representation, such as in the Resource Description Framework (RDF), where they model statements as subject-predicate-object relationships. In this context, a triple like (subject, predicate, object) encodes meaningful assertions about entities in a structured way.

The notation for a triple typically uses parentheses, with elements separated by commas, such as (a, b, c). Unlike sets, triples preserve order and allow repeated elements, distinguishing them from unordered collections. This property makes them versatile for applications requiring precise ordering and repetition, such as database records or structured data formats.