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Continuum (pl.: continua or continuums) theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities. In contrast, categorical theories or models explain variation using qualitatively different states.
Continuum theory of specific heats of solids, see Debye model; Triune continuum, trinity of continual representations in general system modeling defined in the theory of triune continuum, used in the triune continuum paradigm; Continuous spectrum, referred to simply as the continuum in contrast to discrete spectral lines
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a continuous medium (also called a continuum) rather than as discrete particles. Continuum mechanics deals with deformable bodies, as opposed to rigid bodies. A continuum model assumes that the substance of the ...
In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, denoted by . [ 1 ] [ 2 ] Georg Cantor proved that the cardinality c {\displaystyle {\mathfrak {c}}} is larger than the smallest infinity, namely, ℵ 0 {\displaystyle \aleph _{0}} .
Continuum theory is the branch of topology devoted to the study of continua. Definitions. A continuum that contains more than one point is called nondegenerate. A ...
In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line.. Formally, a linear continuum is a linearly ordered set S of more than one element that is densely ordered, i.e., between any two distinct elements there is another (and hence infinitely many others), and complete, i.e., which "lacks gaps" in the sense that every nonempty subset ...
The continuum assumption is an idealization of continuum mechanics under which fluids can be treated as continuous, even though, on a microscopic scale, they are composed of molecules. Under the continuum assumption, macroscopic (observed/measurable) properties such as density, pressure, temperature, and bulk velocity are taken to be well ...
The continuum hypothesis was advanced by Georg Cantor in 1878, [1] and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900. The answer to this problem is independent of ZFC, so that either the continuum hypothesis or its negation can be added as an axiom to ZFC set theory, with the resulting theory being ...