binary operation

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A binary operation or dyadic operation is a calculation that combines two elements
(called operands) to produce another element.
More formally, a binary operation is an operation of arity two.

More specifically, a binary operation on a set is an operation whose two domains and
the codomain are the same set.

Examples include the familiar arithmetic operations of addition, subtraction, multiplication. Other examples are readily found in different areas of mathematics, such as
vector addition, matrix multiplication and conjugation in groups.

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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.[1]

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.

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