| 释义 |
▪ I. factorial, a.1 and n.|fækˈtɔərɪəl|
[f. as prec. + -ial1.]
A. adj.
1. Math. (See quots. and B. a.)
1837Penny Cycl. IX. 155 The term factorial expression has been in some instances applied to an expression of which the factors are in arithmetical progression. 1860G. Boole Calc. Fin. Diff. 6 The term in which they [‘factorials’ in Boole's sense] are involved is called a factorial term. 1867Galbraith Algebra (ed. 3) 396 Factorial functions..If the function consist of equi-different factors.
2. Of or pertaining to a factor (sense 4).
1881Blackie Lay Serm. v. 177 Large farms and factorial management have formed together an unholy alliance.
3. Of or pertaining to a factor (sense 7); factorial analysis = factor analysis.
Quot. 1845 refers to analysis by means of factorials.
[1845T. Tate (title) A treatise on factorial analysis with the summation of series; containing various new developments of functions, &c.] 1935Human Factor IX. 182 With this infinite number of possible factorial analyses of any set of correlations,..a psychologist can find one which agrees with any preconceived notions he may have about the linkages between tests. 1935R. A. Fisher Design Exper. vi. 111 With factorial experiments designed to make a large number of comparisons there will..usually be an ample number of degrees of freedom for the estimation of error. 1949Darlington & Mather Elem. Genetics App. i. 391 Factorial Experiment, one in which all the treatments or agents under investigation are varied simultaneously, and combined in such a way that any derived effect of one or a group of them may be isolated and separately evaluated. 1950Cochran & Cox Exper. Designs v. 124 If all factors are independent in their effects, the factorial approach will result in a considerable saving of the time and material devoted to the experiments. 1971Jrnl. Gen. Psychol. LXXXII. 53 A factorial analysis of covariance was performed on the data for delayed recall.
4. Photogr. Of or pertaining to the determination of the interval of time allowed after the appearance of the image and before the completion of the development of a film.
1910Westm. Gaz. 29 June 16/2 If one be using a factorial system of development it is well to reduce the factor a little, using, say, seven where nine would represent the ordinary time of development.
B. n. Math. [In F. factorielle.]
a. gen. The product of a series of factors in arithmetical progression. In later usage sometimes with wider sense: The product of a series of factors which are similar functions of a variable that changes by a constant difference in passing from any factor to the next. Cf. faculty 2 c.
(Boole Calc. Fin. Diff. 6 defines the word as meaning each of the factors composing such a product, and uses factorial term for what other writers call a factorial.)
1816Herschel in Lacroix's Diff. & Int. Calc. App. §370 Any quantity of the form axn + bxn—1 + etc. may be resolved into factorials. 1845Penny Cycl. Suppl. I. 559 Arbogast..proposed to call the different cases of xn1a by the name of factorials. 1867Galbraith Algebra (ed. 3) 397 To find the difference of a factorial.
b. spec. The product of an integer multiplied into all the lower integers.
For example, the factorial of 6 (written symbolically {fac}6 or 6!) is 6 × 5 × 4 × 3 × 2 = 720. Factorials are of frequent use in the investigation of Permutations and Probabilities.
1869J. J. Raven Ch. Bells Camb. (1881) 77 The number of changes that can be rung on a peal of bells is the factorial of the number of the bells.
▪ II. facˈtorial, a.2 rare.
[f. factory + -al1.]
‘Pertaining to a factory; consisting in a factory’.
1864Webster refers to Buchanan. 1885Science VI. 100 The advisability of..securing a limited district for a..‘factorial establishment’ for American citizens in that region [the Kongo country]. |