assotsiatiivne

Assotsiatiivne is the Estonian term for associative, used primarily in mathematics and related fields. An operation on a set is associative if, for all elements a, b and c in the set, the equation (a * b) * c = a * (b * c) holds. This property means that when an operation is applied to more than two elements, the way in which the operations are grouped does not affect the outcome.

Associativity is distinct from commutativity, which concerns the order of operands rather than grouping. A common way to recognize associativity is to check whether a given operation allows parentheses to be rearranged without changing the result, enabling longer expressions to be evaluated without ambiguity.

Common examples include addition and multiplication of numbers, which satisfy (a + b) + c = a + (b + c) and (ab)c = a(bc). String concatenation is another associative operation: (xy)z = x(yz). Function composition is also associative: (f ∘ g) ∘ h = f ∘ (g ∘ h). Matrix multiplication and set union are additional examples of associative operations in their respective contexts.

Not all operations are associative. Subtraction and division fail the property in general, since (a − b) − c ≠ a − (b − c). In algebra, associativity underpins the structure of monoids and groups, and in computing it enables safe parallelization and simplified evaluation of expressions.

Etymologically, the term derives from Latin associare, indicating joining or putting together, with the Estonian form assotsiatiivne reflecting this origin.