Selectedsuch

Selectedsuch is a term used in some mathematical and computer-science texts to denote a selection operator that forms the subset of elements from a given domain that satisfy a specified predicate. It is essentially a compact way to describe filtering or set comprehension: from a domain D and a predicate P, the result is the set { x in D | P(x) }.

Definition and notation: Selectedsuch(D, P) yields the elements x in D for which P(x) holds. In many informal writings, it is expressed with a function-like syntax such as SelectedSuch(D, x -> P(x)) or simply SelectedSuch(D, P). Conceptually, it mirrors the standard filter operation found in programming languages and the mathematical notion of a subcollection defined by a condition.

Relation to other concepts: Selectedsuch is closely related to filters, list comprehensions, and the selection operator in relational algebra. In practice, it serves as a concise shorthand for selecting elements that meet a criterion, with semantics that align with subset formation. The operator emphasizes the act of choosing elements rather than describing the entire domain.

Examples: Given a list D = {1, 2, 3, 4, 5} and a predicate P(x) = (x is even), Selectedsuch(D, P) would yield {2, 4}. In a database context, Selectedsuch(D, P) might correspond to a query that retrieves records satisfying P.

Status: The term is informal and not part of a standard mathematical or programming vocabulary. It is used descriptively in some texts to discuss the idea of selection by condition. See also: filter, subset, where clause, list comprehension.