| 释义 |
‖ continuum|kənˈtɪnjuːəm|
Pl. continua |-ə|.
[L.; neuter of continuus, i.e. ‘a continuous body or thing’.]
A continuous thing, quantity, or substance; a continuous series of elements passing into each other. space-time continuum, see space-time. Also attrib., as continuum mechanics, continuum theory; continuum hypothesis Math., the hypothesis that there is no transfinite cardinal between the cardinal of the set of positive integers and that of the set of real numbers.
1650Sir T. Browne Pseud. Ep. ii. i. (ed. 2) 40 The fusible salt draws the earth and infusible part into one continuum. 1677Hale Prim. Orig. Man. iv. iv. 327 The admirable accommodation of the several Parts of the Humane Body to make up one Continuum. 1865Grote Plato I. i. 13 There could be no continuum: each numerical unit was distinct and separated from the rest by a portion of vacant space. a1878Lewes Study Psychol. (1879) 133 To these animals [the wolf and dog] the external world seems a continuum of scents, as to man it is a continuum of sights. 1886J. Ward in Encycl. Brit. XX. 51/1 (Psychology) All possible sensations of colour, of tone, and of temperature constitute as many groups of qualitative continua. 1903B. Russell Princ. Math. I. xxxvi. 297 Cantor proves that any series M satisfying the above conditions is ordinally similar to the number-continuum, i.e. the real numbers from 0 to 1, both inclusive. 1905Westm. Gaz. 14 Aug. 2/1 We must know more of the properties of the ponderable atoms moving in the continuum which fills all space. 1924W. B. Selbie Psychol. of Relig. iv. 91 There are no doubt good physiological reasons for these phenomena of the sensory continuum. 1938Proc. Nat. Acad. Sci. XXIV. 101 The continuum hypothesis of Georg Cantor. 1951C. Truesdell in Jrnl. Math. Pures et Appliquées XXX. 116 The notion of an isotropic function..has been much employed in continuum mechanics. Ibid. 150 Continuum theory, being independent of any sort of deterministic mechanics of the ultimate particle, serves as a general guide with which any molecular model must be consistent. 1953A. E. Smailes Geogr. Towns 33 There is no longer either socially or physically a simple clear-cut dichotomy of town and country; rather it is an urban-rural continuum. 1953A. A. Fraenkel Abstract Set Theory ii. 152 The assumption that, for every transfinite t, 2t is the cardinal next larger than t, is called the generalized continuum hypothesis. 1955W. Noll in Jrnl. Rational Mech. & Anal. IV. 12 (heading) Basic concepts of continuum mechanics. 1962L. J. Cohen Diversity of Meaning (1966) i. 12 Descriptive studies are also needed to abstract and record the pivotal stages in a continuum of change. 1964Proc. Nat. Acad. Sci. LI. 109 Since our additional axiom is quite readily acceptable to most mathematicians..one can regard the unprovability of the Continuum Hypothesis as firmly estabished. |