| 释义 |
symmetric, a.|sɪˈmɛtrɪk|
[f. symmetry + -ic, after geometric. Cf. F. symétrique, † symmetrique (1529).]
1. a. = symmetrical.
1796Burney Mem. Metastasio II. 332 The air should be phrased and symmetric. 1816Tuckey Narr. Exped. R. Zaire iii. (1818) 108 The faces of many of the women were by no means unprepossessing, and their forms extremely symmetric. 1853Sylvester in Phil. Trans. CXLIII. 434 Calculating the symmetric functions as a function only of x [etc.]. 1854Cayley Math. Papers II. 233 The covariant may in the former case be called a symmetric covariant, and in the latter case a skew covariant. 1860Tyndall Glac. ii. xxix. 403 The ripples from the two sides form a pair of symmetric curves. 1871Browning Balaust. 1656 While still one's heart, in time and tune, Paced after that symmetric step of Death. 1885Burton Arab. Nts. (1887) III. 12 Perfect in beauty and loveliness and stature and symmetric grace.
b. Math. and Logic. symmetric difference (see quot. 1936); symmetric group, the group of all the permutations of a set of unlike entities.
1936Trans. Amer. Math. Soc. XL. 38 The Union (modulo 2), or symmetric difference, of two classes is the class of objects belonging to one or the other, but not to both, of those classes. 1971J. H. Conway in Powell & Higman Finite Simple Groups vii. 225 If some non-empty {scrC}-set has fewer than five elements, every set of the same cardinal would be a {scrC}-set,..and by taking symmetric differences we should obtain every two-element set..as a {scrC}-set, which cannot be.
1897W. Burnside Theory of Groups of Finite Order viii. 139 The group of order n! which consists of all the substitutions that can be performed on n symbols is called the symmetric group of degree n. 1955L. Mirsky Introd. Linear Algebra ix. 257 In addition to the symmetric group..there are other groups of permutations, all of them naturally subgroups of the symmetric group.
c. Physics. = symmetrical a. 2 b.
1935Condon & Shortley Theory of Atomic Spectra iii. 165 If the atom is at a certain moment in a symmetric state it will always remain in a symmetric state. 1965H. Muirhead Physics Elem. Particles ix. 369 It is apparent from this equation that parallel spin states..are symmetric. 1979Nature 29 Mar. 404/2 Certain baryons..contain three identical quarks with parallel spins in a state which is symmetric (the wave function does not change sign) to the interchange of a pair of quarks.
2. Logic. Of a binary relation: such that when two terms for which it is true are interchanged, it remains true.
1933Mind XLII. 34 Not even God himself can make men into women by shifting words, or make what we call ‘implies’ symmetric by changing names. 1968New Scientist 16 May 339/1 Equality is symmetric as well as being reflexive. 1979K. J. Devlin Fund. Contemp. Set Theory i. 14 A binary relation on a set is an equivalence relation just in case it is reflective, symmetric, and transitive. |