vectorswhether

Vectorswhether is a term used to describe a conceptual object that combines a vector with a boolean predicate. It is not standard in mathematics but can be a useful way to discuss predicate-based vector filtering or conditioning in various contexts.

Definition and concept. A vectorswhether consists of a vector v in a vector space V and a predicate p: V → {true, false} that can be evaluated on v. The essential content is the boolean result p(v), interpreted as a yes/no test about the vector. If the predicate is fixed, the vectorswhether corresponds to the characteristic function χ_S(v) = true if v ∈ S and false otherwise for some subset S ⊆ V. If the predicate depends on parameters or context, one obtains a family of predicates p_θ, producing a corresponding family of vectorswithers.

Examples. In R^2, with p(v) = (||v|| ≤ 1), the vectorswhether is true for vectors inside the unit disk. Another example is p(v) indicating whether v lies within a prescribed angular sector or is within a tolerance of a prescribed direction.

Applications and usage. The concept is useful in computational geometry, data filtering, and boolean masking, where vectors are selected or discarded based on a predicate. It also aligns with ideas in optimization and machine learning where constraints or feasibility checks are applied to vectors.

Relation to related concepts. A vectorswhether is closely related to the indicator or characteristic function of a set, and to the notion of a boolean mask applied to a vector data collection. It is a descriptive device rather than a standard mathematical object with universal notation.

History. The term appears as a coined concept in informal discussions and literature exploring predicate-based vector constructs, rather than as a canonical object with fixed notation. See also: vector space, predicate, indicator function, mask, constraint.