| 单词 | commutative |
| 例句 | Addition of vectors is commutative such that A + B = B + A . College Physics for AP Courses 2015-08-12T00:00:00Z Since changing the order of the subtraction does not give the same result, we know that subtraction is not commutative. Intermediate Algebra 2020-05-06T00:00:00Z In your own words, state the commutative property of addition. Elementary Algebra 2020-04-22T00:00:00Z We have seen that vector addition in two dimensions satisfies the commutative, associative, and additive inverse properties. Calculus, Volume 3 2016-03-30T00:00:00Z Use the following properties of real numbers: commutative, associative, distributive, inverse, and identity. Algebra and Trigonometry 2015-02-13T00:00:00Z Noether’s theory of ideals and commutative rings forms a foundation for any researcher in the field of higher algebra. 3 Revolutionary Women of Mathematics 2022-03-09T05:00:00Z The commutative properties apply only to addition and multiplication! Intermediate Algebra 2020-05-06T00:00:00Z The commutative property has to do with order. Elementary Algebra 2020-04-22T00:00:00Z Unlike most operations we’ve seen, the cross product is not commutative. Calculus, Volume 3 2016-03-30T00:00:00Z It is important to note that neither subtraction nor division is commutative. Algebra and Trigonometry 2015-02-13T00:00:00Z He proposed that a geometric object called a scheme was associated to any commutative ring — that is, a set in which addition and multiplication are defined and multiplication is commutative, a × b = b × a. Alexander Grothendieck (1928-2014) : Nature : Nature Publishing Group 2015-01-13T05:00:00Z Without that breakdown of the commutative law, there would be no Heisenberg uncertainty principle, atoms would collapse, and nothing would exist. Commuting: Steven Strogatz Explains One of the Laws of Multiplication [Excerpt] 2012-10-05T14:15:00.253Z Since changing the order of the subtraction did not give the same result, we know that subtraction is not commutative. Elementary Algebra 2020-04-22T00:00:00Z Often the meaning of a sentence tacitly implies that the commutative law does not hold. The philosophy of B*rtr*nd R*ss*ll 2011-12-30T03:00:24.883Z We find that so the operation of function composition is not commutative. Algebra and Trigonometry 2015-02-13T00:00:00Z But the term commutative has no longer much meaning when applied to the respect due to the life, the liberty, or the honor of others. Elements of Morals With Special Application of the Moral Law to the Duties of the Individual and of Society and the State 2011-08-10T02:00:16.913Z But it’s merely the commutative law in action. Commuting: Steven Strogatz Explains One of the Laws of Multiplication [Excerpt] 2012-10-05T14:15:00.253Z We saw that subtraction and division were not commutative. Elementary Algebra 2020-04-22T00:00:00Z Whoever professes it ought to be learned in the laws, and understand distributive and commutative justice, in order to right all mankind. The History of Don Quixote de la Mancha 2011-05-01T02:00:10.977Z Because matrix multiplication is not commutative, order matters. Algebra and Trigonometry 2015-02-13T00:00:00Z An indication of the specific difference between distributive and commutative justice is that the same individual may be just in private matters and unjust in public matters. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z Fair enough, but that begs the question I’d like to explore in some depth here: Is this commutative law of multiplication, a × b = b × a, really so obvious? Commuting: Steven Strogatz Explains One of the Laws of Multiplication [Excerpt] 2012-10-05T14:15:00.253Z Since changing the order of the division did not give the same result, division is not commutative. Elementary Algebra 2020-04-22T00:00:00Z You should think of this as a generalization of the commutative law for addition of ordinary numbers, x and y, according to which x + y = y + x. Group Think 2010-05-03T11:35:00Z Similarly, the commutative property of multiplication states that numbers may be multiplied in any order without affecting the product. Algebra and Trigonometry 2015-02-13T00:00:00Z But it does not seem that he violates commutative justice, unless the party for whom he could testify has a strict right to the testimony. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z Maybe we’re wired to doubt the commutative law because in daily life, it usually matters what you do first. Commuting: Steven Strogatz Explains One of the Laws of Multiplication [Excerpt] 2012-10-05T14:15:00.253Z The commutative properties only apply to addition and multiplication! Elementary Algebra 2020-04-22T00:00:00Z Negative Numbers may be regarded as resulting from the commutative law for addition and subtraction. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" For instance, consider We begin by using the associative and commutative properties of multiplication to regroup the factors. Algebra and Trigonometry 2015-02-13T00:00:00Z All will depend on the character of the law, whether it is penal or preceptive, and if preceptive, whether it obliges in virtue of legal or of commutative justice. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z It is measured by commutative justice and confers a strict claim to a reward. Grace, Actual and Habitual A Dogmatic Treatise In order to combine like terms in the next example, we will use the commutative property of addition to write the like terms together. Elementary Algebra 2020-04-22T00:00:00Z “Simple” practice involves an application of the commutative law. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" No. Multiplication is commutative, so the order of the factors does not matter. Algebra and Trigonometry 2015-02-13T00:00:00Z If contumely is not contrary to commutative justice, there is no duty of restitution. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z It is measured by commutative justice and thus confers a real claim to a reward. Grace, Actual and Habitual A Dogmatic Treatise When we have to simplify algebraic expressions, we can often make the work easier by applying the commutative or associative property first, instead of automatically following the order of operations. Elementary Algebra 2020-04-22T00:00:00Z Division.—From the commutative law for multiplication, which shows that 3 � 4d. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" These are the commutative properties, the associative properties, the distributive property, the identity properties, and the inverse properties. Algebra and Trigonometry 2015-02-13T00:00:00Z All agree that commutative justice is violated when contumely becomes vilification, or when an insult is committed in the presence of onlookers with the purpose of making the offended person seem contemptible in their eyes. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z Therefore it is evident that both are comprised under commutative justice. Summa Theologica, Part III (Tertia Pars) From the Complete American Edition But external things are the matter of distributive and commutative justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Among equals, it is called commutative justice, the which alone is here in question. Explanation of Catholic Morals A Concise, Reasoned, and Popular Exposition of Catholic Morals This illustrates the fact that matrix multiplication is not commutative. Algebra and Trigonometry 2015-02-13T00:00:00Z Concretely, in cases of property insured, the insured is bound in commutative justice not to deliberately destroy or damage the property covered by the policy under penalty of losing all rights to compensation. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z Our view is that the teaching on usury was simply one of the applications of the doctrine that all voluntary exchanges of property must be regulated by the precepts of commutative justice. An Essay on Mediaeval Economic Teaching Now the rewarding of the good does not belong to a special virtue, but is an act of commutative justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province They may also be designated as commutative, distributive, and universal justice. History of Modern Philosophy From Nicolas of Cusa to the Present Time Every error in commutative justice is an immolation of the laborer, a transfusion of the blood of one man into the body of another. System of Economical Contradictions; or, the Philosophy of Misery Obedience to Tax Laws.—Obedience to just laws is owed either from legal justice alone, or also from commutative justice with the burden of restitution. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z It will be noticed, however, that the principles of commutative justice all treat of the commutations of external goods—in other words, they assume the existence of property of external goods in individuals. An Essay on Mediaeval Economic Teaching Therefore, if distributive and commutative justice have different matters, it would seem that they are not comprised under the same virtue, viz. justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Of commutative justice, in buying dear, I say, upon trust, and selling goods cheap, that is, for ready money. Gargantua and Pantagruel, Illustrated, Book 3 As there is a right to honour and a right to reputation, so insult and detraction are sins, not against charity, but against commutative justice, calling for restitution. Moral Philosophy On the other hand, the duty of religion obliges more strictly than that of commutative justice, and hence it does not seem that grave matter should be the same for both. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z The justification of interest rested on precisely the same ground as the prohibition of usury, namely, the observance of the equality of commutative justice. An Essay on Mediaeval Economic Teaching First we shall consider respect of persons which is opposed to distributive justice; secondly we shall consider the vices opposed to commutative justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Now commutative justice consists in rendering something to one person, while distributive justice consists in giving something to many. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province A contract is a bargain productive of an obligation of commutative justice in each of the contracting parties. Moral Philosophy It differs likewise from commutative justice, which is obligatory in agreements with parents or other superiors, for the duty is then owed them as partners to a free contract. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z In order that such exchange might be justifiable, it must be conducted on a. basis of commutative justice, which, as we have seen, consisted in the observance of equality according to the arithmetical mean. An Essay on Mediaeval Economic Teaching Secondly, it may be considered in view of the form of judgment, in as much as, even in commutative justice, the judge takes from one and gives to another, and this belongs to distributive justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Therefore the mean should also be observed in the same way in both distributive and commutative justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Where there is no explicit contract, the duties which the subjects of a person's official care have towards him are not duties of commutative justice. Moral Philosophy In the second case of striking against different employers, the "sympathizers" are striking against a just employer and are violating their work contract which binds in commutative justice. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z Objection 1: It would seem that the two species of justice are unsuitably assigned, viz. distributive and commutative. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Hence all these actions belong to the one same species of justice, namely commutative justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Objection 1: It would seem that restitution is not an act of commutative justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Distinguished from the other three cardinal virtues is particular justice, which is divided into distributive and commutative justice. Moral Philosophy It is classed under commutative justice on account of the return that is offered for the offense; 2721. Moral Theology A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities 2011-02-24T03:00:54.237Z Now it is an act of commutative injustice to take away what belongs to another. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province This order is directed by commutative justice, which is concerned about the mutual dealings between two persons. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province For distributive justice directs distributions, while commutative justice directs commutations that can take place between two persons. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province This justice is called commutative, from being concerned with exchanges, or contracts, voluntary and involuntary. Moral Philosophy Therefore restitution is not more an act of commutative than of distributive justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Now a person's deserts are considered also in commutative justice, for instance, in punishments; thus a man who strikes a prince is punished more than one who strikes a private individual. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Hence there are two species of justice, distributive and commutative. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Hence in distributive justice a person's station is considered in itself, whereas in commutative justice it is considered in so far as it causes a diversity of things. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province This is the obligation of restitution, which attaches to breaches of commutative justice, and, strictly speaking, to them alone. Moral Philosophy In all these cases, however, repayment must be made on a basis of equality according to the requirements of commutative justice, namely that the meed of passion be equal to the action. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Therefore the matters of distributive and commutative justice are not distinct. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province Objection 1: It would seem that the mean in distributive justice is to be observed in the same way as in commutative justice. Summa Theologica, Part II-II (Secunda Secundae) Translated by Fathers of the English Dominican Province The second way in which commutative justice binds you to positive action, is when undue damage is likely to occur to another from some activity of yours. Moral Philosophy The old notion, that Justice is minding your own business, and leaving your neighbour to mind his, furnishes a good rough statement of the obligations of commutative justice. Moral Philosophy But if the fire has broken out from my careless use of fire, commutative justice binds me to raise the alarm. Moral Philosophy Aristotle speaks of "corrective," not of "commutative" justice. Moral Philosophy |
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