Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Continuous |
ContinuousAdjective1. Continuing in time or space without interruption; "a continuous rearrangement of electrons in the solar atoms results in the emission of light"- James Jeans; "a continuous bout of illness lasting six months"; "lived in continuous fear"; "a continuous row of warehouses"; "a continuous line has no gaps or breaks in it"; "moving midweek holidays to the nearest Monday or Friday allows uninterrupted work weeks". 2. (mathematics) of a function or curve; extending without break or irregularity. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "continuous" was first used in popular English literature: sometime before 1321. (references) |
Etymology: Continuous \Con*tin"u*ous\, adjective. [Latin expression continuus, from continere to hold together. See Continent.]. (references) |
| Domain | Definition |
Mathematics | Of a parameter or random variable that may take any value in a range. Source: European Union. (references) |
Tips from 1870 | Usage: Continual, Continuous. Continuous implies uninterrupted, unbroken. Continual relates to acts that are frequently repeated. "The continuous ride is often finished in five hours, but owing to continual delays we were eight hours on the way." Source: Slips of Speech. |
Source: compiled by the editor from various references; see credits. | |
(From Wikipedia, the free Encyclopedia)
1. See Continuity (mathematics).
2. In film, continuity is consistency of the positions, colors, sizes, etc., of objects onscreen; continuity errors break the illusion of watching actual events. Care towards continuity must be taken because films are rarely, if ever, filmed in the order they are presented in: that is, a crew may film a scene from the end of a movie first, followed by one from the middle; the shooting schedule is sometimes dictated by weather, permitting issues, or other circumstances besides preference. Frequently film shoots will have a person dedicated exclusively to minding continuity.
One example of broken continuity occurs in the 1998 film Waking Ned Devine, when two of the characters are walking through a storm to Ned's house: the umbrella they are under is black during their conversation on the walk to the house (filmed from slightly above and to the front); yet after cutting to a lower shot from behind of Jackie approaching the house, Michael walks onscreen from the right holding an umbrella that is not black but beige, with a brown band at the rim.
Continuity also matters in other forms of art, such as novels and comics. If a character loses his jacket in one scene, yet he is still wearing it in a later scene without recovering it or getting another one, that is a break in continuity.
In a larger sense, continuity refers to consistent details of any fictional world, such as the names of characters' relatives.
Accidental or deliberate discrepancies in continuity are known as retconning, which stands for "retroactive continuity."
See also Krypto-Revisionism.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Continuity."
(From Wikipedia, the free Encyclopedia)
In topology, a continuous function is generally defined as one for which preimages of open sets are open. Continuous functions are fundamental in describing the relationships between topological spaces, and allow simple generalizations of many results from real analysis to be proven. Because this definition only "uses" open sets, this makes continuity of a function a topological property, depending only on the topologies of its domain and range spaces.
Formulations of Continuity
Several equivalent formulations of continuity can be made, and each is useful in different situations. Similar to the open set formulation is the closed set formulation, which says that preimages of closed sets are closed.
Definition based on preimages are often difficult to use directly. Instead, suppose we have a function f from X to Y, where X,Y are topological spaces. We say f is continuous at x for some if for any neighborhood V of f(x), there is a neighborhood U of x such that . Although this definition appears complex, the intuition is that no matter how "small" V becomes, we can find a small U containing x that will map inside it. If f is continuous at every , then we simply say f is continuous.
In a metric space, it is equivalent to consider only open balls centered at x and f(x) instead of all neighborhoods. This leads to the standard delta-epsilon definition of a continuous function from real analysis, which says roughly that a function is continuous if all points close to x map to points close to f(x). This only really makes sense in a metric sense, however, which has a notion of closeness.
Useful properties of continuous maps
Some facts about continuous maps between topological spaces:
- If f : X → Y and g : Y → Z are continuous, then so is the composition g o f : X → Z.
- If f : X → Y is continuous and
- X is compact, then f(X) is compact.
- X is connected, then f(X) is connected.
- X is path-connected, then f(X) is path-connected.
- If f : X → Y and X is a metric space, then we also have:
- If a sequence (xn) converges to a limit x, then the sequence (f(xn)) obtained by applying f to each element converges to f(x). We say continuous functions take limits to limits. When using netss instead of sequences, this holds for a general topological space X.
Other notes
If a set is given the discrete topology, all functions with that space as a domain are continuous. If the domain set is given the trivial topology, a topology with only two open sets, and the range set is T1, then only constant functions are continuous.
Symmetric to the concept of a continuous map is an open map, for which images of open sets are open. In fact, if an open map f has an inverse, that inverse is continuous, and if a continuous map g has an inverse, that inverse is open.
If a function is a bijection, then it has an inverse function. The inverse of a continuous bijection need not be continuous, but if it is, this special function is called a homeomorphism.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Continuity (topology)."
(From Wikipedia, the free Encyclopedia)
In mathematics, a continuous function is one in which "small" changes in the input produce "small" changes in the output. If small changes in the input can produce a broken jump in the changes of the output, the function is said to be discontinuous (or to have a discontinuity).
As an example, consider the function h(t) which describes the height of a growing child at time t. This function is continuous (unless the child's legs were amputated). As another example, if T(x) denotes the air temperature at height x, then this function is also continuous. In fact, there is the dictum in nature everything is continuous. By contrast, if M(t) denotes the amount of money in a bank account at time t, then the function jumps whenever money is deposited or withdrawn, so the function M(t) is discontinuous.
For continuity as it is used in topology, see continuity (topology).
Real valued continuous functions
Suppose we have a function that maps real numbers to real numbers and is defined on some interval, like the three functions h, T and M from above. Such a function can be represented by a graph in the cartesian plane; the function is continuous if, roughly speaking, the graph is a single unbroken curve with no "holes" or "jumps": if it can be drawn by hand without lifting the pencil from the paper.
To be more precise, we say that the function f is continuous at some point c if the following three requirements are satisfied:
We call the function everywhere continuous, or simply continuous, if it is continuous at every point of its domain.
- f(c) must be defined (i.e. c must be an element of the domain of f)
- The limit of f(x), as x approaches c, must exist
- The limit of f(x), as x approaches c, must equal f(c)
Epsilon-delta definition
Without resorting to limits, one can define continuity of real functions as follows.
Again consider a function f that maps a set of real numbers to another set of real numbers, and suppose c is an element of the domain of f. The function f is said to be continuous at the point c if (and only if) the following holds: For any positive number ε however small, there exists some positive number δ such that for all x with c - δ < x < c + δ, the value of f(x) will satisfy f(c) - ε < f(x) < f(c) + ε. This "epsilon-delta definition" of continuity was first given by Cauchy.
More intuitively, we can say that if we want to get all the f(x) values to stay in some small neighborhood around f(c), we simply need to choose a small enough neighborhood for the x values around c, and we can do that no matter how small the f(x) neighborhood is.
Examples
- All polynomials are continuous, and so are the exponential functions, logarithms, square root function and trigonometric functions.
- The absolute value function is also continuous.
- An example of a discontinuous function is the function f defined by f(x) = 1 if x > 0, f(x) = 0 if x ≤ 0. Pick for instance ε = 1/2. There is no δ-neighborhood around x=0 that will force all the f(x) values to be within ε of f(0). Intuitively we can think of a discontinuity as a sudden jump in function values.
Facts about continuous functions
If two functions f and g are continuous, then f + g and fg are continuous. If g(x) ≠ 0 for all x in the domain, then f/g is also continuous.
The composition f o g of two continuous functions is continuous.
The intermediate value theorem is an existence theorem, based on the real number property of completeness, and states: "If the real-valued function f(x) is continuous on the closed interval [a, b] and k is some number between f(a) and f(b), then there is some number c in [a, b] such that f(c) = k. For example, if a child undergoes continuous growth from 1m to 1.5m between the ages of 2 years and 6 years, then, at some time between 2 years and 6 years of age, the child's height must have equalled 1.25m.
As a consequence, if f(x) is continuous on [a, b] and f(a) and f(b) differ in sign, then, at some point c, f(c) must equal zero.
If a function f is defined on a closed interval [a,b] and is continuous there, then the function attains its maximum, i.e. there exists c∈[a,b] with f(c) ≥ f(x) for all x∈[a,b]. The same is true for the minimum of f. (Note that these statements are false if our function is defined on an open interval (a,b). Consider for instance the continuous function f(x) = 1/x defined on the open interval (0,1).)
If a function is differentiable at some point c of its domain, then it is also continuous at c. The converse is not true: a function that's continuous at c need not be differentiable there. Consider for instance the absolute value function at c=0.
Continuous functions between metric spaces
Now consider a function f from one metric space (X, dX) to another metric space (Y, dY). Then f is continuous at the point c in X if for any positive real number ε, there exists a positive real number δ such that all x in X satisfying dX(x, c) < δ will also satisfy dY(f(x), f(c)) < ε.
This can also be formulated in terms of sequences and limits: the function f is continuous at the point c if and only if for every sequence (xn) in X with limit lim xn = c, we have lim f(xn) = f(c). Continuous functions transform limits into limits.
This latter condition can be weakened as follows: f is continuous at the point c if and only if for every convergent sequence (xn) in X with limit c, the sequence (f(xn)) is a Cauchy sequence. Continuous functions transform convergent sequences into Cauchy sequences.
See also:
- uniform continuity
- bounded linear operator
- absolute continuity
- semicontinuity
References
- Visual Calculus by Lawrence S. Husch, University of Tennessee (2001)
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Continuous function."
(From Wikipedia, the free Encyclopedia)
A continuous game, or real-time game, is a game without pauses, turns, rounds, or other stopping points.The term is only used of video games, which are today almost all real-time, the shift having proceeded gradually through the 1980s and 1990s, partly enabled by increases in computing power.
The relatively new video game genre known as real-time strategy modified traditional strategy games in a way that brought public attention to the differences between real-time and turn-based games.
Examples of some real-time strategy games are Command and Conquer, Red Alert, StarCraft, and Age of Empires.
Compare turn-based game.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Continuous game."
(From Wikipedia, the free Encyclopedia)
By one convention, a random variable X is called continuous if its cumulative distribution function is continuous. That is equivalent to saying that Pr[X = a] = 0 for all real numbers a, i.e.: the probability that X attains the value a is zero, for any number a.While for a discrete random variable one could say that an event with probability zero is impossible, this can not be said in the case of a continuous random variable, because then no value would be possible.
This paradox is solved by realizing that the probability that X attains a value in an uncountable set (for example an interval) can not be found by adding the probabilities for individual values.
By another convention, the term "continuous random variable" is reserved for random variables that have probability density functions. A random variable with the Cantor distribution is continuous according to the first convention, and according to the second, is neither continuous nor discrete nor a weighted average of continuous and discrete random variables.
In practical applications random variables are often either discrete or continuous.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Continuous random variable."
(From Wikipedia, the free Encyclopedia)
See:
- Continuum (mathematics)
- Continuum hypothesis
- Continuum mechanics
- Generalized continuum hypothesis
- Time-space continuum
- Continuum computer game
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Continuum."
(From Wikipedia, the free Encyclopedia)
In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions that are used in various parts of mathematics, like products and inverse limits. Accordingly, the dual notion of a colimit, or directed limit, generalizes disjoint unions and direct sums. Limits and colimits have strong relationships to the categorial concepts of universal morphisms and adjoint functors.
Definition
Before defining limits, it is useful to define the auxiliary notion of a cone of a functor. Therefore consider two categories J and C and a covariant functor F : J-> C. A cone of F is an object L of C, together with a family of morphisms φX : L -> F(X) for every object X of J, such that for every morphism f : X -> Y in J, we have F(f) o φX = φY. This situation may be depicted as a commutative diagram, more precisely as a commutative triangle with the vertices L, F(X), and F(Y). Indeed the (usually infinite) collection of all these triangles can be (partially) depicted in the shape of a cone with the point L.
A limit of a functor is just a universal cone. In detail, a cone (L, φX) of a functor F : J-> C is a limit iff for any cone (N, ψX) of F, there exists precisely one morphism u : N -> L such that φX o u = ψX for all X. We may say that the morphisms ψX factor through L with the unique factorization u.
As in the case of unique morphisms, this definition describes a balanced state of generality: The limit object L has to be sufficiently specific, in order to meet the requirement of being a cone. On the other hand, L has to be more general than any other such cone to allow for a unique factorization.
It is possible that a functor does not have a limit at all. However, if a functor has two limits then there exists a unique isomorphism between the respective limit objects, which is given by the unique factorization from one limit to the other. Thus limits are unique up to isomorphism and can be denoted by lim F.
Examples
In spite of the generality of the definition of limits, a number of special limits have been emphasized since they represent cases that can be found in many practical settings. In the following we will consider the limit (L, φX) of a functor F : J -> C.
Products. If J is a discrete category, i.e. if J has only the identity morphisms, then the L is called a product. The special case where J consists of just two objects (which we will call 1 and 2) then defines a binary product. For example, assume that C is the category Set and let J be the discrete two-element category. The binary product L will then just be the cartesian product F(1) x F(2) in Set. The morphisms φ1 and φ2 are the projections to the respective components of the tuples from L. This generalizes to arbitrary small categories J and arbitrary (infinite) cartesian products.
Another well-known product is the product topology in Top. If a partially ordered set is viewed as a category, then products are greatest lower bounds while arbitrary cones are just lower bounds. In many algebraic contexts, such as (abelian) groups, rings , boolean algebras, etc., products are just cartesian products, where the operations are defined pointwise.
Terminal object. If J is the empty category that contains no objects, then clearly the above definitions imply that every object of C is a cone of F. A limit then is an object that has a unique factorization through any other object. This is just the definition of a terminal object.
Equalizers. If J is a two-element category with two parallel morphisms from object 1 to object 2 then the limit L is called an equalizer. Practical examples of these constructions are considered in the article on equalizers.
Kernels. The special case of an equalizer where one of the morphisms is mapped to a zero morphism, the resulting limit is called a kernel.
Pullbacks. Let J be a category with the three elements a, b and c, where the only non-identity morphisms are f : a -> c and g : b -> c. The limit L is then called a pullback or a fibred product. It can nicely be visualized as a commutative square, with the diagonal φc = F(f) o φa = F(g) o φb.
All of the above examples follow a common scheme for the definition of limits: in order to model a limit construction, such as a product of sets, one uses a functor that "picks out" the relevant objects (and sometimes morphisms) from the category C. Consequently, the category J usually is small and has viewer elements than the category C. If one considers a finite category J then the above constructions can also be specified by giving the objects and morphisms that the functor F maps to. For example one may talk about an "equalizer of two morphisms" instead of calling this limit an "equalizer of a functor that maps the only two non-trivial morphisms in J to certain values".
However, J may well be a large category, i.e. one that has a proper class of objects. For example, the product of all sets exists and is just the empty set (indeed, this is the only possible cone on all families of sets that contain the empty set).
Complete categories
A limit of a functor F : J-> C is called small iff the category J is small. Similarly, a limit is finite if J is. A category C is called complete iff every functor F : J-> C, where J is small, has a limit, i.e. if all small limits in this category exist. Many important categories are complete: groups, abelian groups, sets, modules over some ring, topological spaces and compact Hausdorff spaces. The Existence Theorem for Limits states that a category is complete iff it has equalizers and arbitray (infinite) products.
It turns out that the property of having all (even large) limits is too strong to be practically relevant. Any category with this property necessarily is of a very restricted form: for any two objects there can be at most one homorphism from one object to the other.
If J is a small category and every functor from J to C has a limit, then the limit operation forms a functor from the functor category CJ to C. For example, if J is a discrete category and C is the category Ab of abelian groups, then lim : AbJ -> Ab is the functor which assigns to every J-indexed family of abelian groups its direct product. More generally, if J is a small category arising from a partially ordered set, then lim: AbJ -> Ab assigns to every system of abelian groups its inverse limit.
Functors and limits
It is a natural question to ask, which functors are compatible with the construction of limits in the sense that they map limits to limits. These functors are called continuous or limit preserving. Formally, a functor G : C -> D is continuous iff, for every small category I and every functor F : I -> C that has a limit (L,φX) in C, the functor GF : I -> D has the limit (G(L), G(φX) ). Since the Existence Theorem for Limits shows that all limits can be expressed by products and equalizers, it is sufficient for continuity if G preserves these special limits.
Important examples of continuous functors are given by representable ones: if U is some object of C, then the functor GU : C -> Set with GU(V) = MorD(U, V) for all objects V in D is continuous.
The importance of adjoint functors lies in the fact that every functor which has a left adjoint (and therefore is a right adjoint) is continuous. In the category Ab of abelian groups, this for example shows that the kernel of a product of homomorphisms is naturally identified with the product of the kernels. This illustrates that one may also say that a continuous functor commutes with the construction of limits.
Being a universal construction, limits also have other strong relationships to adjoint functors. The limit functor lim : CJ -> C (if it exists) has as left adjoint the diagonal functor C -> CJ which assigns to every object N of C the constant functor whose value is always N on objects and idN on morphisms. In particular, limit functors are continuous.
Colimits
The dual notion of limits and cones are colimits and co-cones. Although it is straightforward to obtain these definitions by inverting all morphisms in the above definitions, we will explicitly state them here:
Consider two categories J and C and a covariant functor F : J-> C. A co-cone of F is an object L of C, together with a family of morphisms φX : F(X) -> L for every object X of J, such that for every morphism f : X -> Y in J, we have φX o F(f)= φY. Again, a visualization of this situation resembles a cone (this time pointing downwards).
A colimit of a functor is a universal co-cone: a co-cone (L, φX) of a functor F : J-> C is a colimit iff for any co-cone (N, ψX) of F, there exists precisely one morphism u : L -> N such that u o φX = ψX for all X. If it exists, the colimit of F is unique up to a unique isomorphism and is denoted by colim F.
Limits and colimits are related as follows: A functor F : J -> C has a colimit if and only if for every object N of C, the functor X |-> MorC(F(X),N) (which is a covariant functor on the dual category Jop) has a limit. If that is the case, then
for every object N of C.
- MorC(colim F, N) = lim MorC(F(-), N)
The category C is called cocomplete if every functor F : J -> C with small J has a colimit. The following categories are cocomplete: sets, groups, abelian groups, modules over some ring and topological spaces.
A covariant functor that commutes with the construction of colimits is said to be cocontinuous or to preserve colimits. Every functor which has a right adjoint (and is a left adjoint) is cocontinuous. As an example in the category Grp of groups the functor F : Set -> Grp which assigns to every set S the free group over S has a right adjoint (the forgetfull functor Grp -> Set) and is therefore cocontinuous.
The dual versions of the above examples are coproducts, initial objects, coequalizers, cokernels, and pushouts, respectively.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Limit (category theory)."
| The following table is compiled from various sources, across various languages. When English abbreviations or acronyms come from a non-English source, this is noted. | |||
| Entry | Source | Expression | Field |
| COD | English | Continuous Optical Discharge | Physics |
| CONS | French | Continuous | Transportation |
Source: compiled by the editor, based on several corpora (additional references). | |||
Synonym: ContinuousSynonym: uninterrupted (adj). (additional references) |
| Antonym: discontinuous (adj). (additional references) |
| Context | Synonyms within Context (source: adapted from Roget's Thesaurus). |
Continuity | Adjective: continuous, continued; consecutive; progressive, gradual; serial, successive; immediate, unbroken, entire; linear; in a line, in a row; Noun: uninterrupted, unintermitting; unremitting, unrelenting (perseverence) a; perennial, evergreen; constant. |
| Source: adapted from Roget's Thesaurus. | |
| Domain | Usage | |
Screenplays | It was playing continuous, no intermission (The Owl and the Pussycat; writing credit: Buck Henry; Bill Manhoff) | |
Movie/TV Titles | The Continuous Woman (1973) | |
Source: compiled by the editor from various references; see credits. | ||
| Domain | Title | ||
References |
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Books | |||
Periodicals |
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Theater & Movies | |||
Music |
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High Tech |
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Consumer Goods |
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Source: compiled by the editor from various references; see credits. | |||
| Thumbnail | Description & Credit | Thumbnail | Description & Credit |
 | Line drawing showing the lining of the GI tract: colorectal (muscularis). The walls of the digestive tract have four layers of tissue: mucosa, submucosa, muscularis externa and serosa. The inner-most layer is the mucosa, a membrane that forms a continuous lining of the GI tract from the mouth to the anus. In the large bowel, this tissue contains cells that produce mucus to lubricate and protect the smooth inner surface of the bowel wall. Connective tissue and muscle separate the muscosa from the second layer, the submucosa, which contains blood vessels, lymph vessels, nerves and mucus-producing glands. Next to the submucosa is the muscularis externa, consisting of two layers of muscle fibers-one that runs lengthwise and one that encircles the bowel. The fourth layer, the serosa, is a thin membrane that produces fluid to lubricate the outer surface of the bowel so that it can slide against adjacent organs. Credit: Unknown photographer/artist. |  | Raydist strip chart record used to keep track of individual navigation rates These strip charts required continuous monitoring by a watch-stander Used to assure navigational accuracy during hydrographic surveying operations First tests of Raydist on SOSBEE in 1954 Used for over 40 years with various systems. Credit: Coast & Geodetic Survey Historical Image Collection. |
 | 808 fathometer transducer Hydrographic Manual 1942 Called first portable sonic sounding device First acoustic sounding device used on C&GS sounding boats for shallow water First use of shallow water fathometer continuous records by C&GS. Credit: Coast & Geodetic Survey Historical Image Collection. |  | Setting up planting sites at Barren Island for patchy and continuous planting areas. The sites were marked and designated in advance. Credit: NOAA Restoration Center. |
 | The plantings were conducted in different patterns to determine the most successful planting technique. The technique in the foreground is a checkerboard planting, the middle area is unplanted, and the background planting was done as a continuous planting. The best success was in high density patchy plantings. Credit: NOAA Restoration Center. |  | Figure 4. A lead fish used for continuous sounding operations at slow speed. This device was invented in 1914 and improved by Pierre Marti in 1920. Credit: Sailing for Science - the NOAA Fleet Then and Now. |
 | Figure 63. Marti's continuous recording sounder built by the French engineer Pierre Marti. In 1919, Marti began designing and describing sounding machines based on acoustic methods. This recording device allowed measuring time of sound emanation and time of reception, thus giving travel time which can be used to determine depth. Credit: Sailing for Science - the NOAA Fleet Then and Now. |  | Little Blue River continuous CRP tree planting by farmers and volunteers. Kansas. Credit: Jeff Vanuga. |
 | Grass filter strip in Carroll County, Iowa. Established as part of the continuous signup in the Conservation Reserve Program. Credit: Lynn Betts. |  | Collecting and freely sharing plants and seeds that grow around the world is one of the U.S. Department of Agriculture's longest continuous programs. P. Credit: USDA ARS News; photo by Scott Bauer.. |
Source: pictures compiled by the editor from various references; see picture credits. | |||
 |  |
| "_TRANSPORT:47" by Janus R. Sørensen Commentary: "We all live in a world of interconnection... a world of continuous dynamicism... a world of perpetual and neverending information transport. In order for our socitey to thrive, we must communicate. New ideas, concepts, and feelings all transverse the gl" | "Rose border" by Roger Kirby Commentary: "This is intended for use as a border for media, when replicated verticaly it forms a continuous image." |
Source: photographs selected by the editor, with permission from the photographers. | |
| Author | Quotation |
Author Unknown | Courtesy should be a continuous action, not something to be turned on and off like a faucet. |
Baruch Spinoza | What everyone wants from life is continuous and genuine happiness. Happiness is the rational understanding of life and the world. |
James Whitcomb Riley | Continuous, unflagging effort, persistence and determination will win. Let not the man be discouraged who has these. |
Johann Wolfgang Von Goethe | Austere perseverance, hash and continuous... rarely fails of its purpose, for its silent power grows irresistible greater with time. |
John Keats | Wide sea, that one continuous murmur breeds along the pebbled shore of memory! |
Schiller | Genuine morality is preserved only in the school of adversity; a state of continuous prosperity may easily prove a quicksand to virtue. |
Source: compiled by the editor from various references. | |
| Author | Date | Quotation |
Treaty of Versailles | 1919 | Germany undertakes that German wagons shall be fitted with apparatus allowing: (1) of their inclusion in goods trains on the lines of such of the Allied and Associated Powers as are parties to the Berne Convention of May 15, 1886, as modified on May 18, 1907, without hampering the action of the continuous brake which may be adopted in such countries within ten years of the coming into force of the present Treaty, and (2) Of the acceptance of wagons of such countries in all goods trains on the German lines. (reference) |
Winston S. Churchill | 1946 | Neither the sure prevention of war, nor the continuous rise of world organization will be gained without what I have called the fraternal association of the English-speaking peoples. ("Iron Curtain" Speech) |
Source: compiled by the editor from various references. | ||
| Title | Author | Quote |
Les Miserables | Hugo, Victor | He directed everything by a sort of invisible and continuous magnetic action |
Source: compiled by the editor from various references. | ||
| Subject | Topic | Quote |
Health | The pressure is constant and continuous. (references) | |
Pain is continuous and may be heightened by emotional stress. (references) | ||
These practices help reduce the risk of continuous self reinfection. (references) | ||
Business | The average age is 10 years and needing continuous repairs. (references) | |
Furthermore, bulk transport enables a continuous flow of supply for processing. (references) | ||
The local representative can provide continuous support during the evaluation period. (references) | ||
Children | Sierra Leone | Legal requirements for naturalization, such as continuous residence in the country for 15 years or the past 12 months and 15 of the previous 20 years, effectively deny citizenship to many long-term residents, notably the Lebanese community. (references) |
Civil Liberties | Czech Republic | In one case a Slovak applicant was denied Czech citizenship illegally then required to leave the Czech Republic, thus losing his continuous resident status and voiding his citizenship claim. (references) |
Japan | The laws are subject to review, including possible repeal, in 2005. The Public Security Investigation Agency placed Aum Shinrikyo/Aleph under continuous surveillance for a 3-year period on January 31, 2000, on the basis of one of the new laws. (references) | |
Economic History | Uk | The UK economy has enjoyed eight years of continuous growth. (references) |
Lebanon | In October 2000, the BSE instituted computerized continuous trading. (references) | |
Guyana | There is a continuous decline in rice production, as much as 25% in some areas. (references) | |
Human Rights | Indonesia | In addition unverified reports of provocations and conspiracies fueled the continuous cycle of violence. (references) |
Kyrgyz Republic | Human rights groups operated in a hostile environment and were faced with continuous government pressure to curtail their activities. (references) | |
Lebanon | The Chairman of the Commission subsequently stated that "the health conditions of the prisoners are deplorable and require continuous care. (references) | |
Minorities | Japan | By law aliens with 5 years of continuous residence are eligible for naturalization and the simultaneous acquisition of citizenship rights, including the right to vote; however, in practice most eligible aliens choose not to apply for citizenship, in part due to fears that their cultural identity would be lost. (references) |
Hong Kong | In August, the U.N. Committee on the Elimination of Racial Discrimination expressed its concern about "the continuous absence of legal provisions protecting persons from racial discrimination to which they may be subjected by private persons, groups or organizations." The Committee rejected the Government's argument that such laws should not be initiated just because they might not be supported by society as a whole. (references) | |
Political Economy | Austria | After a continuous rise in popularity the FPO received 27 percent of the votes in the 1999 elections, slightly ahead of the OVP. (references) |
Political Rights | Zambia | Provisions for a continuous registration system were enacted too late to be of use in the December 27 elections. (references) |
Trade | Spain | Spain has a single computerized and centralized continuous stock market in which insider trading is penalized. (references) |
Denmark | The credit line is typically extended on a continuous, revolving basis and is not subject to an annual settlement. (references) | |
Travel | Brazil | They prefer a more continuous working relationship. (references) |
Venezuela | Many stores and businesses, particularly in the larger cities, are changing to a continuous operating schedule, but it is still best to ask for the hours of operation. (references) | |
Costa Rica | Typical working hours are 8:00 AM to 12:00 PM and 2:00 PM to 6:00 PM. The Costa Rican government has a continuous working schedule from 7:30 AM to 4:00 PM. Most banks are open from 9:00 AM to 3:00 PM. (references) | |
Women | Jordan | The husbands themselves must apply for citizenship after fulfilling a requirement of 15 years of continuous residence. (references) |
Worker Rights | United Kingdom | Parental leave provisions are available for employees with more than a year's continuous service. (references) |
Jordan | Workers may not work more than 10 hours in any continuous period or more than 60 hours of overtime per month. (references) | |
Lexicography | Devil's Dictionary | GUNPOWDER, n. An agency employed by civilized nations for the settlement of disputes which might become troublesome if left unadjusted. By most writers the invention of gunpowder is ascribed to the Chinese, but not upon very convincing evidence. Milton says it was invented by the devil to dispel angels with, and this opinion seems to derive some support from the scarcity of angels. Moreover, it has the hearty concurrence of the Hon. James Wilson, Secretary of Agriculture. Secretary Wilson became interested in gunpowder through an event that occurred on the Government experimental farm in the District of Columbia. One day, several years ago, a rogue imperfectly reverent of the Secretary's profound attainments and personal character presented him with a sack of gunpowder, representing it as the sed of the Flashawful flabbergastor, a Patagonian cereal of great commercial value, admirably adapted to this climate. The good Secretary was instructed to spill it along in a furrow and afterward inhume it with soil. This he at once proceeded to do, and had made a continuous line of it all the way across a ten-acre field, when he was made to look backward by a shout from the generous donor, who at once dropped a lighted match into the furrow at the starting-point. Contact with the earth had somewhat dampened the powder, but the startled functionary saw himself pursued by a tall moving pillar of fire and smoke and fierce evolution. He stood for a moment paralyzed and speechless, then he recollected an engagement and, dropping all, absented himself thence with such surprising celerity that to the eyes of spectators along the route selected he appeared like a long, dim streak prolonging itself with inconceivable rapidity through seven villages, and audibly refusing to be comforted. "Great Scott! what is that?" cried a surveyor's chainman, shading his eyes and gazing at the fading line of agriculturist which bisected his visible horizon. "That," said the surveyor, carelessly glancing at the phenomenon and again centering his attention upon his instrument, "is the Meridian of Washington." H |
Source: compiled by the editor from ICON Group International, Inc.; see credits. | ||
| Speaker | Term | Phrase(s) |
John F. Kennedy | 1961-1963 | In a word, Cuba was under the continuous threat of aggressive forces, which did not conceal their intention to invade its territory. |
Source: compiled by the editor from various references. | ||
| "Continuous" is generally used as an adjective (general or positive) -- approximately 99.96% of the time. "Continuous" is used about 2,647 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted) |
| Parts of Speech | Percent | Usage per 100 Million Words | Rank in English |
| Adjective (general or positive) | 99.96% | 2,646 | 3,463 |
| Noun (plural) | 0.04% | 1 | 339,140 |
| Total | 100.00% | 2,647 | N/A |
Source: compiled by the editor from several corpora; see credits.
Expressions using "continuous": Continuous brake ♦ continuous cloud ♦ continuous continuous casting ♦ continuous conveyor ♦ continuous current ♦ continuous file ♦ continuous fire ♦ continuous form ♦ continuous function ♦ continuous hyperthermic peritoneal perfusion ♦ continuous illumination fire ♦ Continuous impost ♦ continuous infusion ♦ continuous load ♦ continuous paper ♦ continuous path control of motion ♦ continuous performance ♦ continuous process control ♦ continuous processor ♦ continuous production shop ♦ continuous rated torque ♦ continuous receiver watch ♦ continuous stall current ♦ continuous strip camera ♦ continuous strip imagery ♦ continuous strip photography ♦ continuous system ♦ continuous System Modeling Program ♦ continuous tense ♦ continuous wave ♦ Dodge continuous sampling plan ♦ limiting continuous thermal withstand value ♦ maximum continuous power and thrust ♦ modulated continuous wave ♦ permanent continuous casting ♦ temporally continuous process ♦ total continuous spectrum noise. Additional references. | |
| Hyphenated Usage | |
Beginning with "continuous": continuous-calibration, continuous-composite, continuous-extraction, continuous-feed, continuous-flow, continuous-flow water heater, continuous-movement, continuous-operations, continuous-process, continuous-speech, continuous-sprung, continuous-wave, continuous-welding. | |
Ending with "continuous": near-continuous, semi-continuous. | |
| Source: compiled by the editor from various references; see credits. | |
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Language | Translations for "continuous"; alternative meanings/domain in parentheses. | |
Afrikaans | vas (abiding, constant, continual, lasting, permanent, sustained), permanent (abiding, constant, constantly, continual, continually, continuously, lasting, permanent, sustained), aanhoudend (abiding, constant, continual, lasting, permanent, sustained, unceasing), aanhoudelik (abiding, lasting). (various references) | |
Albanian | i vazhdueshëm (ceaseless, chronic, constant, continual, continued, endless, frequent, incessant, lingering, niggling, non-stop, perennial, permanent, perpetual, persistent, regular, running, steady, unbroken, uninterrupted), i vazhduar (extended, unceasing, uninterrupted), i pashkëputur (uninterrupted), i pandërprerë (ceaseless, continual, entire, incessant, inseverable, perpetual, solid, sustained, unceasing, uniform, uninterrupted, unremitting). (various references) | |
Arabic | متواصل (ceaseless, constant, continual, continued, incessant, persistent, round the clock, running, unbroken, unceasing, uninterrupted, unremitting), تواصلية. (various references) | |
Bulgarian | непрекъснат (continual, everlasting, incessant, permanent, perpetual, running, solid, sustained, unceasing, uninterrupted, unremitting), продължителен (chronic, durable, enduring, extended, lingering, long, long standing, long-drawn, progressive, prolonged, protracted, sustained, unbroken), прав (direct, erect, flat, forehanded, right, stand up, standing, straight, swerveless, undeviating, unseated, upright, upstanding), постоянен (abiding, changeless, chronic, constant, direct, firm, fixed, frequent, hourly, immovable, invariable, lasting, minutely, perennial, permanent, perpetual, persistent, regular, secular, settled, stable, standing, static, steadfast, steady, stock, substantive, sustained, unalterable, undeviating, unfailing, unidirectional, uniform, uninterrupted, unvaried). (various references) | |
Chinese | 連續 (in a row), 连续 (Continual, Continuance, Continuously, sequential, serial, succession, successive), 繹 (explain, unravel), 不斷 (constant, unceasing, uninterrupted). (various references) | |
Czech | plynulý (flowing, fluent, fluid), permanentní (permanent), nepřetržitý (continual, incessant, solid, steady, unbroken, unceasing, uninterrupted), nepřerušovaný. (various references) | |
Danish | uafbrudt (abiding, lasting, unceasing, uninterrupted), kontinuerlig (persistent). (various references) | |
Dutch | onafgebroken (lasting, unceasing, uninterrupted), doorlopend (unceasing, uninterrupted), ononderbroken (at a strech, for ... together, on end, unceasing, uninterrupted), continu (lasting), aanhoudend (abiding, constant, lasting, sustained, unceasing). (various references) | |
Esperanto | seninterrompa, senhalta (non-stop). (various references) | |
Faeroese | framhaldandi (lasting). (various references) | |
Farsi | متوالی (Consecutive, Reel, Uninterrupted), مداوم (Ongoing, Stable, Steady, Unremitting). (various references) | |
Finnish | yhtenäinen (connected, consistent, homogeneous, uniform), yhtämittainen (unbroken, uninterrupted), yhtäjaksoinen (unbroken, uninterrupted), taukoamaton (incessant, uninterrupted), keskeytymätön (unbroken, uninterrupted), katkeamaton (unbroken, uninterrupted), jatkuva (constant, continual, continued, uninterrupted), herkeämätön (incessant, steady, unceasing), alituinen (continual, incessant, perpetual). (various references) | |
French | permanent (constant, continual), continu. (various references) | |
German | kontinuierlich (continuing, uninterrupted), ununterbrochen (continually, continuously, incessant, incessantly, non-stop, solid, solidly, steadily, steady, unbroken, uninterrupted), stetig (constant, continual, continuing, continuously, even, permanent, steady, sustained), fortlaufend (consecutive, consecutively, consecutivly, continual, ongoing, progressional, progressive, regular, running, serial). (various references) | |
Greek | συνεχήσ (consecutive, constant, continual, cursive, successive, unremitting), συνεχής (constant, continual, sustained, unfailing), επίμονος (intractable, persevering, persistent, pertinaceous, tenacious), αδιάκοποσ (constant, incessant, pauseless, unbroken, unceasing, uninterrupted, unrelenting), διαρκής (abiding, longstanding, persistent). (various references) | |
Hebrew | תמידי (constant, incessant, permanent, persistent, unfailing), רציף (serial, successive), רצוף (attached, consecutive, enclosed, flooring, inlaid, paved, paving, running, sequential, successive, unbroken, uninterrupted), נמשך (abiding, attracted, consequent, continued, enduring, gravitate, lasting, protracted). (various references) | |
Hungarian | folyamatos (consecutive, Imperfective, perpetual, persistent, running, sequential, uninterrupted). (various references) | |
Indonesian | berkesinambungan (uninterruptedly), berkepanjangan (prolonged, protracted), aduk-adukan (mixing). (various references) | |
Italian | continuo (abiding, ceaseless, continual, hourly, incessant, lasting, non-stop, running, steady). (various references) | |
Japanese Kanji | 連綿たる (unbroken, uninterrupted), 脈脈たる (pulsating forcefully, unbroken), 脈脈 (ceaseless), 継続的 , 綿綿たる (endless), 持続的 , ぶっ通し (complaining in a small voice, grumbling, to collide with, to strike). (various references) | |
Japanese Katakana | ぶっとおし, れんめんたる (unbroken, uninterrupted), めんめんたる (endless), けいぞくてき, じぞくてき, みゃくみゃくたる (pulsating forcefully, unbroken), みゃくみゃく (ceaseless). (various references) | |
Korean | 끊임없는 (incessant, Perpetual). (various references) | |
Manx | kinjagh (ballast, ballast of person, constant, continual, definite, incessant, invariable, persistent, regular, steady, unceasing, unfailing), gyn scuirr (ceaseless, endless, everlasting, everlastingly, non-stop, perpetual). (various references) | |
Papiamen | durabel (abiding, lasting). (various references) | |
Pig Latin | ontinuouscay.(various references) | |
Polish | trwały (abiding, lasting). (various references) | |
Portuguese | contínuo (attendant, constant, continual, continue, enduring, eternal, lasting, never-ceasing, ongoing, permanent, perpetual, persistent, progressive, round, running, runny, sequential, solid, straight, sustained, thru, unbroken, unceasing, uninterrupted, unremitting). (various references) | |
Romanian | continuu (ceaseless, continual, continually, continuously, hourly, incessant, perpetual, running, sustained, unbroken, unceasing, uninterrupted, unremitting), veşnic (always, continual, endless, eternal, eternally, everlasting, inextinguishable, livelong, never-dying, perdurable, perennial, perennially, perpetual, perpetually, sempiternal, unceasing), progresiv (gradual, gradually, progressive, progressively), neîntrerupt (unbroken, uninterrupted, uninterruptedly, without intermission), neîncetat (ceaseless, ceaselessly, continual, continually, endless, incessant, invariably, never ending, never-ceasing, relentless, restlessly, sabbathless, unbroken, unceasing, unending, unremitting). (various references) | |
Russian | непрерывный (ceaseless, contiguous, continual, continued, incessant, indiscrete, on-the-fly, perpetual, sustained, unbroken, unceasing, uninterrupted). (various references) | |
Scottish | sgairneach (a continuous heap of loose stones on a hill side), sgàirneach (a continuous heap of loose), beiceartaich (nf.ind. a continuous becking or bobbing). (various references) | |
Serbo-Croatian | trajan (abiding, durable, fast, imperfective, lasting, livelong, perdurable, permanent), stalan (abiding, constant, continual, on-going, perm, permanent, regular, stabile, steady), neprekidan (ceaseless, continual, incessant, non-stop, on-going, round the clock, sustained, sustaining, unresting). (various references) | |
Spanish | continuo (abiding, chronic, constant, continual, direct, lasting, nagging, non-stop, permanent, perpetual, persistent, rolling, steady, sustained, unbroken, unceasing, uninterrupted). (various references) | |
Swedish | oupphörlig (ceaseless, constant, continual, incessant, lasting, perpetual, sustained, unceasing), oavbruten (continual, sustained, unbroken, unceasing, unimpeded, uninterrupted, unrelieved), kontinuerlig, ihållande (continual, incessant, insistent, pertinacious). (various references) | |
Turkish | zincirleme, sürekli (abiding, assiduous, chronic, consistent, consistently, constant, continual, continuum, durable, enduring, everlasting, habitual, hourly, imprescriptible, incessant, invariable, lasting, non-stop, perennial, permanent, perpetual, persistent, running, secular, settled, standing, steady, sustained, unabating, unceasing, unremitting), devamlı (assiduous, away, chronic, continual, continued, everlasting, evermore, forever, frequent, hourly, in ordinary, incessant, invariable, invariably, lasting, non-stop, on end, permanent, persistent, regular, regularly, settled, steady, sustained, unabating, unbroken, unceasing, unremitting), devam eden (continued, continueing, run on), aralıksız (continued, incessant, non-stop, perpetual, sustained, unabating, unbroken, unceasing, uninterrupted, unremitting, without a respite, without interruption, without space). (various references) | |
Turkmen | birsyhly. (various references) | |
Ukrainian | суцільний (entire, integrate, one piece, pieceless, solid), тривалий (continued, extended, lasting, lingering, livelong, long, long term, protracted, slow, spacious, sustained, voluminous, yearlong), безперервний (ceaseless, continual, continued, entire, incessant, never ending, never-ceasing, ongoing, perpetual, unceasing, uninterrupted). (various references) | |
Vietnamese | liên tiếp (consecutive, continuously, reel), liên tục (cease, consecutive, continual, continuously, endless, reel, running, sequent, sequential, together, unceasing, unintermittent, unremitting), không dứt (ceaseless, constant, incessant, truceless, unceasing, unending). (various references) | |
Welsh | di-fwlch (without a break). (various references) | |
| Source: compiled by the editor from various translation references. | ||
| Language | Period | Translations |
| Greek | 700 BCE-300 CE | hektikos. (various references) |
| Latin | 500 BCE-Modern | contexta, contextarum, contextum, continens, continentem, continentes, continentia, continentis, continuo, continuum, continuus, iugis iuge, perpetua, perpetuae, perpetuo, perpetuum, perpetuus. (various references) |
| Source: compiled by the editor from various references. | ||
Derivations | |
Words beginning with "continuous": continuously, continuousness, continuousnesses. (additional references) | |
Words ending with "continuous": discontinuous, noncontinuous. (additional references) | |
Words containing "continuous": discontinuously. (additional references) | |
| |
"Continuous" is suggested in spellcheckers for the following: coninuous, contangos, contenious, contignuous, contineous, continguous, continious, continous, continuence, continueos, continuos, continuouse, Continuus, contiquous. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "continuous" (pronounced kunti"nyuwus) |
| 5 | -n y uw u s | disingenuous, ingenuous, strenuous. |
| 4 | -y uw u s | ambiguous, conspicuous, contiguous, innocuous, vacuous. |
| 3 | -uw u s | arduous, contemptuous, deciduous, incongruous, tempestuous, tumultuous, virtuous. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "c-i-n-n-o-o-s-t-u-u" | |
-1 letter: continuos, contusion, innocuous. | |
-2 letters: continuo, unctions. | |
-3 letters: nocuous, nonsuit, notions, nuncios, suction, uncinus, unction. | |
-4 letters: coitus, conins, contos, counts, cousin, cutins, nitons, nostoc, notion, nuncio, onions, outsin, tocsin, tonics, tunics, unions, unison. | |
-5 letters: cions, coins, conin, conns, conto, conus, coons, coots, count, cutin, cutis, icons, ictus, incus, niton, noons, nouns, onion, ontic, scion, scoot, scout. | |
| Words containing the letters "c-i-n-n-o-o-s-t-u-u" | |
+2 letters: continuously. | |
+3 letters: countinghouse, discontinuous, noncontiguous, noncontinuous, uncontentious. | |
+4 letters: contiguousness, continuousness, countinghouses. | |
+5 letters: counterquestion, discontinuously. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
| 1. Definition 2. Synonyms 3. Crosswords 4. Usage: Modern | 5. Usage: Commercial 6. Images: Slideshow 7. Images: Photo Album 8. Images: Digital Art | 9. Quotations: Familiar 10. Quotations: Historic 11. Quotations: Fiction 12. Quotations: Non-fiction | 13. Quotations: Speeches 14. Usage Frequency 15. Expressions 16. Expressions: Internet | 17. Translations: Modern 18. Translations: Ancient 19. Abbreviations 20. Acronyms | 21. Derivations 22. Rhymes 23. Anagrams 24. Bibliography |
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