“binary operation”的概念、定义、翻译、参考文献-科学参考

binary operation

Mathematics

A binary operation ○ on a set S is a rule that associates with any elements a and b of S an element denoted by a ○ b. This is equivalent to saying that S is closed under ○. Common examples include addition, multiplication, and composition (on certain sets). See associative, commutative, operation.

Computer

1. (dyadic operation) defined on a set S. A function from the domain S×S into S itself. Many of the everyday arithmetic and algebraic operations are binary, including the addition of two integers, the union of two sets, and the conjunction of two Boolean expressions.
Although basically functions, binary operations are usually represented using an infix notation, as in
$3 + 4, U \cup V, P \land Q$
The operation symbol then appears between the left and right operand. A symbol, such as °, can be used to represent a generalized binary operation.
When the set S is finite, Cayley tables and sometimes truth tables are used to define the meaning of the operation.
2. An operation on binary operands.

Philosophy

A function of two arguments. Addition is a binary operation, i.e. x+y is a function from the two numbers x, y, to a third number, which is their sum.

单词	binary operation
释义	binary operation Mathematics A binary operation ○ on a set S is a rule that associates with any elements a and b of S an element denoted by a ○ b. This is equivalent to saying that S is closed under ○. Common examples include addition, multiplication, and composition (on certain sets). See associative, commutative, operation. Computer 1. (dyadic operation) defined on a set S. A function from the domain S×S into S itself. Many of the everyday arithmetic and algebraic operations are binary, including the addition of two integers, the union of two sets, and the conjunction of two Boolean expressions. Although basically functions, binary operations are usually represented using an infix notation, as in $3 + 4, U \cup V, P \land Q$ The operation symbol then appears between the left and right operand. A symbol, such as °, can be used to represent a generalized binary operation. When the set S is finite, Cayley tables and sometimes truth tables are used to define the meaning of the operation. 2. An operation on binary operands. Philosophy A function of two arguments. Addition is a binary operation, i.e. x+y is a function from the two numbers x, y, to a third number, which is their sum.
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