éénnaaréén

éénnaaréén is a coined term used to denote a one-to-one correspondence between two sets. In Dutch usage, the standard expressions are één-op-één or één-tot-één, but the combined form éénnaaréén can appear in stylized writing or introductory explanations to signal that each element of a source set is paired with a unique element of a target set, and that every target element receives a partner.

In mathematics, this relation is known as a bijection or a bijective function. Formally, a function f from A to B is bijective if it is injective (one-to-one) and surjective (onto). A bijection creates a perfect pairing between elements of the two sets, with no left-overs on either side.

For finite sets, bijectivity implies equal cardinalities: if A and B are finite and f is bijective, then the sets have the same size and every element of A is matched with a distinct element of B. For infinite sets, bijections also demonstrate equivalence of size; for example, there is a bijection between the natural numbers and the even numbers via n ↦ 2n.

Applications of the concept span various fields. In mathematics, it underpins the formal study of functions and mappings. In computer science and database design, bijections describe unambiguous encodings and primary-key mappings. In linguistics and logic, one-to-one correspondences model precise pairings between symbols, sounds, or propositions.

Related terms include injection (one-to-one but not necessarily onto), surjection (onto but not necessarily one-to-one), and broader notions like isomorphism and permutation. The core idea remains a clear, reversible pairing between elements of two sets.