binary operation

Noun

Meaning

an operation that follows the rules of Boolean algebra; each operand and the result take one of two values

Synonyms

Hypernyms

Examples

A groupoid can be seen as a: * Group with a partial function replacing the binary operation ; * Category in which every morphism is invertible. Source: Internet

A natural example is strings with concatenation as the binary operation, and the empty string as the identity element. Source: Internet

Formal definitions In a unital magma Let be a set closed under a binary operation (i. Source: Internet

Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). Source: Internet

In the same way, one defines the binary operation of division ÷ in terms of the assumed binary operation of multiplication and the implicitly defined operation of "reciprocal" (multiplicative inverse). Source: Internet

Suppose that we wish to prove a statement about an n-ary operation implicitly defined from a binary operation, using mathematical induction on n. In this case it is natural to take 2 for the induction basis. Source: Internet

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