Definition & Betydelse | Engelska ordet ASSOCIATIVITY

Definition av ASSOCIATIVITY

1. (matematik) associativitet

Exempel på hur man kan använda ASSOCIATIVITY i en mening

• In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
• Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity.
• They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative.
• The associativity is not important (in fact not used at all) in the definition of a graded ring; hence, the notion applies to non-associative algebras as well; e.
• By inspection, we can determine associativity and closure; note in particular that (ba)b = bab = b(ab).
• Furthermore, associativity does not imply commutativity either – for example multiplication of quaternions or of matrices is always associative but not always commutative.
• Given a polynomial expression, one can compute the expanded form of the represented polynomial by expanding with the distributive law all the products that have a sum among their factors, and then using commutativity (except for the product of two scalars), and associativity for transforming the terms of the resulting sum into products of a scalar and a monomial; then one gets the canonical form by regrouping the like terms.
• Operator associativity determines what happens when an operand is surrounded by operators of the same precedence, as in 1-2-3: An operator can be left-associative, right-associative, or non-associative.
• In mathematics, an H-space is a homotopy-theoretic version of a generalization of the notion of topological group, in which the axioms on associativity and inverses are removed.
• associativity: Within an expression containing two or more of the same associative connectives in a row, the order of the operations does not matter as long as the sequence of the operands is not changed.
• The position of the operator with respect to its operands may be prefix, infix or postfix, and the syntax of an expression involving an operator depends on its arity (number of operands), precedence, and (if applicable), associativity.
• L2 cache increased from 64k to 128k, with associativity increased from 16-way set associative in C3 to 32-way set associative in C7.
• The hyperbolic quaternions form a nonassociative ring; the failure of associativity in this algebra curtails the facility of this algebra in transformation theory.
• Any subtrees may be parenthesized, but often only the right-side subtrees are parenthesized, with left associativity implied for any unparenthesized applications.
• However, Cayley tables can also be used to characterize the operation of a quasigroup, which does not assume associativity as an axiom (indeed, Cayley tables can be used to characterize the operation of any finite magma).
• This is because they can equivalently be defined in terms of the algebraic operations: x∨y = inf(x,y) and x∧y = sup(x,y), subject to certain axioms (commutativity, associativity, absorption and idempotency).
• In the case where the two monoidal products coincide and the distributivities are taken from the associativity isomorphism of the single monoidal structure, one obtains autonomous categories.
• Pointwise operations inherit such properties as associativity, commutativity and distributivity from corresponding operations on the codomain.
• Karabyts' vocal-symphonic works tend to conceptual concreteness, entertainment, achieved by dramaturgical functions of the narrator, independent and rather active role of the poetic component, program accuracy of musical expression, genre associativity, timbre dramaturgy, etc.
• Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity.

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