Iterated binary operation

In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. Common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation. Other operations, e.g., the set theoretic operations union and intersection, are also often iterated, but the iterations are not given separate names. In print, summation and product are represented by special symbols; but other iterated operators often are denoted by larger variants of the symbol for the ordinary binary operator. Thus, the iterations of the four operations mentioned above are denoted

More generally, iteration of a binary function is generally denoted by a slash: iteration of ${\displaystyle f}$ over the sequence ${\displaystyle (a_{1},a_{2}\ldots ,a_{n})}$ is denoted by ${\displaystyle f/(a_{1},a_{2}\ldots ,a_{n})}$, following the notation for reduce in Bird–Meertens formalism.

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