| 单词 | commutative principle |
| 释义 | > as lemmascommutative principle 2. Relating to or involving substitution or interchange; as the commutative principle in arithmetic and algebra, i.e. the principle by which the order of terms or factors may be altered. ΘΚΠ the world > time > change > alternation > [adjective] > alternating interchangeable1561 interchanginga1586 vicissitudinary1624 alternanta1638 reciprocalc1645 alternating1653 up and down1812 intercurrent1842 commutative1844 the world > time > change > exchange > [adjective] > performed by anagrammatical1678 commutative1844 the world > time > change > exchange > substitution > [adjective] substitutional1721 substitutionary1772 commutative1844 the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > principle or rule in commutative principle1876 commutation rule1935 1844 Philos. Trans. (Royal Soc.) 134 225 The commutative law, whose expression is πρu = ρπu. 1857 B. Price Treat. Infinitesimal Calculus (ed. 2) I. xix. 601 If the two operations indicated by ϕ and ψ are performed successively on u, one on the back of the other, let us assume the result to be the same whatever is the order in which they are performed: two such symbols of operation are said to be commutative, and to satisfy the law of commutation. 1876 T. Hill True Order Stud. 42 The commutative principle of arithmetic may be shown by dividing six into three twos, etc. 1964 E. Bach Introd. Transformational Gram. vii. 159 Ordinary arithmetical multiplication and addition form groups of a special character called commutative (or Abelian) groups, since they obey the commutative law. 1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. Algebra iii. 76 A ring in which multiplication is commutative is called a commutative ring. < as lemmas |
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