continuumn.
/kənˈtɪnjʊəm/, U.S. /kənˈtɪnjəwəm/ A continuous thing, quantity, or substance; a continuous series of elements passing into each other. space-time continuum, see space-time adj. and n.
ΘΚΠ
the world > relative properties > order > order, sequence, or succession > continuity or uninterruptedness > [noun] > continuous succession > a continuous series or course
seriousnessc1487
continuity1601
train1606
series1613
thread1642
continuum1650
clue1656
run1709
1650 Sir T. Browne Pseudodoxia Epidemica (ed. 2) ii. i. 40 The fusible salt draws the earth and infusible part into one continuum.
a1676 M. Hale Primitive Originat. Mankind (1677) iv. iv. 327 The admirable accommodation of the several Parts of the Humane Body to make up one Continuum.
1865 G. Grote 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.
a1878 G. H. Lewes 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.
1886 J. Ward in Encycl. Brit. XX. 51/1 [article Psychology] All possible sensations of colour, of tone, and of temperature constitute as many groups of qualitative continua.
1903 B. Russell Princ. Math. 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.
1905 Westm. Gaz. 14 Aug. 2/1 We must know more of the properties of the ponderable atoms moving in the continuum which fills all space.
1924 W. B. Selbie Psychol. Relig. iv. 91 There are no doubt good physiological reasons for these phenomena of the sensory continuum.
1953 A. 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.
1962 L. 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.
Compounds
C1. attributive, as continuum mechanics, continuum theory.
ΚΠ
1951 C. Truesdell in Jrnl. Math. Pures et Appliquées XXX. 116 The notion of an isotropic function..has been much employed in continuum mechanics.
1951 C. Truesdell in Jrnl. Math. Pures et Appliquées XXX. 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.
1955 W. Noll in Jrnl. Rational Mech. & Anal. 4 12 (heading) Basic concepts of continuum mechanics.
C2.
continuum hypothesis n. Mathematics 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.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > branch or theory relating to
syntax1861
set theory1936
continuum hypothesis1938
1938 Proc. National Acad. Sci. U.S.A. 24 101 The continuum hypothesis of Georg Cantor.
1953 A. 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.
1964 Proc. National Acad. Sci. U.S.A. 51 109 Since our additional axiom is quite readily acceptable to most mathematicians..one can regard the unprovability of the Continuum Hypothesis as firmly estabished.
This entry has not yet been fully updated (first published 1893; most recently modified version published online March 2022).
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