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In mathematics, a binary operation or dyadic operation is a rule for combining 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
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Xem thêmMore precisely, a binary operation on a set S is a mapping of the elements of the Cartesian product S × S to S:
Because the result of performing the operation on a pair of elements of S is again an element of S, the...
Xem thêmTypical examples of binary operations are the addition (+) and multiplication (×) of numbers and matrices as well as composition of functions on a single set. For instance,
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Xem thêmA binary operation, ab, depends on the ordered pair (a, b) and so (ab)c (where the parentheses here mean first operate on the ordered pair (a, b) and
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Xem thêmAn external binary operation is a binary function from K × S to S. This differs from a binary operation on a set in the sense in that K need not be S; its elements come from outside.
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Xem thêmBinary operations are often written using infix notation such as a ∗ b, a + b, a · b or (by juxtaposition with no symbol) ab rather than by functional
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Xem thêmA binary operation f on a set S may be viewed as a ternary relation on S, that is, the set of triples (a, b, f(a,b)) in S × S × S for all a and b in S.
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Binary operation - Simple English Wikipedia, the free ...
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 …
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