Continuum

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continuum

(kŏn-tin -yoo-ŭm) The continuous spectrum that would be measured for a body if no absorption or emission lines were present.

Continuum

 

in mathematics a term used to denote structures that have certain properties of continuity [see (1) and (2) below for complete formulations] and to denote [not quite consistently in view of (2) below] the real numbers in discussing their cardinality.

(1) The most throughly studied continuous structure in mathematics is the system of real numbers, the number continuum. The properties of continuity of the system of real numbers can be characterized by different methods (using different “axioms of continuity”). If the concept of inequality (a < b) is used as the fundamental concept, then the continuity of the number continuum can be characterized, for example, by the following two statements: (a) between any two numbers a and b, where a < b, there lies at least one other number c (such that a < c < b ) and (b) if all the numbers are divided into two (nonempty) classes A and B such that every number a of A is less than any number b of B, then there exists either a greatest number in A or a least number in B (Dedekind’s axiom of continuity).

(2) In topology, which is the study of the geometry of continuity, the properties of the continuity of space or of any set are formulated using the concept of limit point. The fundamental concept of the connectivity of a set lying in a topological space (or of all space) is defined as follows: A set M is called connected if for any partition of M into two disjoint and nonempty subsets A and B there is at least one point that belongs to one of them and is a limit point of the other. In topology any connected compact Hausdorff space is called a continuum. Among sets on a line or in n -dimensional Euclidean space, the compact sets are the closed bounded sets. Thus, in Euclidean space a continuum can be defined as a connected closed bounded set. In particular, the only compact sets on the number line are closed intervals (that is, sets of numbers satisfying inequalities of the type a ≤ x ≤ b. In the strict sense of the topological definition of a continuum, the set of all real numbers is not a continuum.

(3) The cardinal number of the set of real numbers is called the cardinal number of the continuum and is denoted by either the Gothic letter C or by the Hebrew letter aleph א (without a subscript, in contrast to the other cardinal numbers). Every topological continuum has the same cardinal number C. The cardinal number C is greater than the cardinal number א0 of countable sets. The continuum problem consists in deciding whether the cardinal number of the continuum is the next cardinal number after א0

continuum

[kən′tin·yə·wəm]
(mathematics)
A compact, connected set.

Continuum

Starting in Windows 10, Continuum is a feature for hybrid and convertible laptops that automatically adjusts the user interface to Tablet Mode. When the keyboard is detached or flipped over, apps are run full screen and the Start screen is displayed rather than the traditional Start menu. Continuum can also be configured to prompt the user before switching modes. See Windows 10.
References in classic literature ?
The whole district north of the Vindhias is the theatre of incessant murders and pillage.
A blind Fate, a vast pitiless Mechanism, seemed to cut and shape the fabric of existence and I, Moreau (by his passion for research), Montgomery (by his passion for drink), the Beast People with their instincts and mental restrictions, were torn and crushed, ruthlessly, inevitably, amid the infinite complexity of its incessant wheels.
Very dimly I began to see the Morlocks about me--three battered at my feet--and then I recognized, with incredulous surprise, that the others were running, in an incessant stream, as it seemed, from behind me, and away through the wood in front.
The intellectual side of man already admits that life is an incessant struggle for existence, and it would seem that this too is the belief of the minds upon Mars.
And who knows (there is no saying with certainty), perhaps the only goal on earth to which mankind is striving lies in this incessant process of attaining, in other words, in life itself, and not in the thing to be attained, which must always be expressed as a formula, as positive as twice two makes four, and such positiveness is not life, gentlemen, but is the beginning of death.
Whoever had selected this retired portion of the grounds as the boundary of a walk, or as a place for meditation, was abundantly justified in the choice by the absence of all glare, the cool, refreshing shade, the screen it afforded from the scorching rays of the sun, that found no entrance there even during the burning days of hottest summer, the incessant and melodious warbling of birds, and the entire removal from either the noise of the street or the bustle of the mansion.
The steel ramrods clanked and clanged with incessant din as the men pounded them furiously into the hot rifle barrels.
Elizabeth would not oppose such and injunction-- and a moment's consideration making her also sensible that it would be wisest to get it over as soon and as quietly as possible, she sat down again and tried to conceal, by incessant employment the feelings which were divided between distress and diversion.
The incessant breezes, however, which sweep these vast plains render the heats endurable.
The living in incessant noise was, to a frame and temper delicate and nervous like Fanny's, an evil which no superadded elegance or harmony could have entirely atoned for.
As for the cardinal, who was lying on his bed with a weary and careworn face, his cards were held by the Comtesse de Soissons, and he watched them with an incessant look of interest and cupidity.
The rains for five months, from the middle of October to the middle of March, are almost incessant, and often accompanied by tremendous thunder and lightning.