- a law asserting that the order in which certain logical operations are performed is indifferent.[1835-45]
* * *Two closely related laws of number operations.In symbols, they are stated: a + b = b + a and ab = ba. Stated in words: Quantities to be added or multiplied can be combined in any order. More generally, if two procedures give the same result when carried out in arbitrary order, they are commutative. Exceptions occur (e.g., in vector multiplication). See also associative law, distributive law.
* * *in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba. From these laws it follows that any finite sum or product is unaltered by reordering its terms or factors. While commutativity holds for many systems, such as the real or complex numbers, there are other systems, such as the system of n × n matrices or the system of quaternions, in which commutativity of multiplication is invalid. Scalar multiplication of two vectors (to give the so-called dot product) is commutative (i.e., a·b = b·a), but vector multiplication (to give the cross product) is not (i.e., a × b = −b × a). The commutative law does not necessarily hold for multiplication of conditionally convergent series. See also associative law; distributive law.
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commutative law — noun : a law applicable to certain mathematical operations: the order of the elements involved is immaterial * * * Logic. a law asserting that the order in which certain logical operations are performed is indifferent. [1835 45] * * * commutative … Useful english dictionary
commutative law — komutatyvumo dėsnis statusas T sritis automatika atitikmenys: angl. commutative law vok. kommutatives Gesetz, n rus. коммутативный закон, m; переместительный закон, m pranc. loi de commutativité, f ryšiai: sinonimas – perstatomumo dėsnis … Automatikos terminų žodynas
commutative law — law asserting that the order in which certain operations is performed is indifferent (Mathematics) … English contemporary dictionary
commutative law — /kəˈmjutətɪv lɔ/ (say kuh myoohtuhtiv law), /ˈkɒmjəteɪtɪv/ (say komyuhtaytiv) noun Logic, Mathematics a law asserting that the order in which certain logical operations are performed is indifferent; in mathematics the two commutative laws are… … Australian English dictionary
commutative contract — see contract Merriam Webster’s Dictionary of Law. Merriam Webster. 1996 … Law dictionary
commutative justice — >> justice. Webster s New World Law Dictionary. Susan Ellis Wild. 2000 … Law dictionary
commutative — index convertible, mutual (reciprocal) Burton s Legal Thesaurus. William C. Burton. 2006 … Law dictionary
commutative contracts — are those in which what is done, given, or promised by one party is considered as an equivalent to or in consideration of what is done, given, or promised by the other. See also commutative and independent contracts … Black's law dictionary
Law — /law/, n. 1. Andrew Bonar /bon euhr/, 1858 1923, English statesman, born in Canada: prime minister 1922 23. 2. John, 1671 1729, Scottish financier. 3. William, 1686 1761, English clergyman and devotional writer. * * * I Discipline and profession… … Universalium
commutative and independent contracts — Commutative contracts are those in which what is done, given, or promised by one party is considered as an equivalent to or in consideration of what is done, given, or promised by the other. Independent contracts are those in which the mutual… … Black's law dictionary