Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Continuously |
ContinuouslyAdverb1. At every point; "The function is continuously differentiable". 2. With unflagging resolve; "dance inspires him ceaselessly to strive higher and higher toward the shining pinnacle of perfection that is the goal of every artiste". Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "continuously" was first used in popular English literature: sometime before 1550. (references) |
(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."
| 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 |
| COLTS | English | Continuously Offered Longer-Term Securities | Finance |
Source: compiled by the editor, based on several corpora (additional references). | |||
Synonyms: ContinuouslySynonyms: ceaselessly (adv), endlessly (adv), incessantly (adv), unceasingly (adv), unendingly (adv). (additional references) |
| Context | Synonyms within Context (source: adapted from Roget's Thesaurus). |
Continuity | Adverb: continuously; Adjective: seriatim; in a line; Noun: in succession, in turn; running, gradually, step by step, gradatim, at a stretch; in file, in column, in single file, in Indian file. |
| Source: adapted from Roget's Thesaurus. | |
Crosswords: Continuously |
| English words defined with "continuously": agitate, American forge, Astronomical time, autoloading, away ♦ Basso continuo, bedrest, blepharism, Bougainvillea glabra ♦ Cable road, campaign, Concrete sound or movement of the voice, Continuedly, crusade ♦ drum roll ♦ escalator ♦ feed, feed in, fight, flow, flowing ♦ Glissette ♦ Kinetoscope ♦ monitor, moving staircase, moving stairway ♦ On and on, Organ point ♦ paper flower, paradiddle, press, push ♦ Range work, reciprocating engine, right along, roll, Ruba-dub ♦ sampling frequency, self-loading, Self-registering, semiautomatic, shifting, stream, streaming ♦ throstle, Tide gauge, To sail on a rhumb, tootle ♦ unstilted. (references) |
| Specialty definitions using "continuously": continuously moving form, continuously set vector. (references) |
| Domain | Title | ||
Books |
| ||
Music |
| ||
Source: compiled by the editor from various references; see credits. | |||
| Thumbnail | Description & Credit | Thumbnail | Description & Credit |
 | The first image obtained from a GOES satellite. These satellites are put in geostationary orbit over 22, 000 miles from Earth and continuously monitor a significant portion of a hemisphere of the Earth. Credit: NOAA in Space. |  | In many people, increased pressure inside the eye causes glaucoma. In the front of the eye is a space called the anterior chamber. A clear liquid flows continuously in and out of this space and nourishes nearby tissues. Credit: National Eye Institute, National Institutes of Health. |
 | During the operation vital information on the patient's condition is projected continuously ... / WHO p. Credit: National Library of Medicine; photo by J. Mohr.. |  | Tennessee Valley Authority production. Chemical plants. Studies in the high-pressure synthesis of gases are being made continuously in the TVA laboratories in the Muscle Shoals area. The plants served by these laboratories make ammonia for conversion into. Credit: Library of Congress. |
Source: pictures compiled by the editor from various references; see picture credits. | |||
 |
| "Japanese rose" by I Y Commentary: "This plant blooms continuously in summer, on the balcony of some very good friends of mine." |
Source: photographs selected by the editor, with permission from the photographers. |
| Author | Quotation |
Thucydides | Peace is an armistice in a war that is continuously going on. |
Source: compiled by the editor from various references. | |
| Title | Author | Quote |
So Long, and Thanks For All the Fish | Douglas Adams | He didn't like to think of himself as the sort of person who giggled or sniggered, but he had to admit that he had been giggling and sniggering almost continuously for well over half an hour now. |
Source: compiled by the editor from various references. | ||
| Subject | Topic | Quote |
Health | Possible drug use during treatment must be monitored continuously. (references) | |
Spasticity is a condition in which certain muscles are continuously contracted. (references) | ||
A clear fluid flows continuously in and out of this space and nourishes nearby tissues. (references) | ||
Business | New products are continuously introduced which command a better market demand. (references) | |
Under such circumstances, the PVC building material consumption has continuously increased rapidly. (references) | ||
Added to this are higher input costs, especially in terms of the continuously rising price of diesel. (references) | ||
Civil Liberties | Czech Republic | However, the law only provides for citizenship for those who have resided continuously in the country since 1993. Roma activists claimed that some local officials refused to process Czech citizenship applications for "Slovak" or stateless Roma families in violation of the law. (references) |
Belize | In 1999 the Government instituted a 6-week amnesty initiative whereby undocumented migrants were eligible to obtain legal residency, provided: They had lived in the country continuously for 4 years; married a Belizean citizen or had a stable common-law association; had Belizean children; or, if female, were at least 4 months pregnant. (references) | |
Economic History | Slovak Rep | Slovakia's population density continuously decreases to the east. (references) |
Human Rights | Pakistan | In this manner, rolling charges can be used to hold a suspect in custody continuously. (references) |
Namibia | The plaintiffs included Tuhafeni Hamwaama, who was kept in leg chains continuously for 11 months. (references) | |
Indonesia | Under the government-sponsored transmigration program, large numbers of persons were moved voluntarily from overpopulated areas to more isolated and less developed areas (this program began during the Dutch colonial period and has been carried out more or less continuously since then). (references) | |
Political Economy | Ireland | The Irish military has been a continuously active participant in UN peacekeeping operations since the mid-1950s. (references) |
Syria | A state of emergency law has been in place almost continuously since 1963, and grants broad powers to the numerous security services. (references) | |
Botswana | Festus Mogae became President in 1998 and continued to lead the Botswana Democratic Party (BDP), which has held a majority of seats in the National Assembly continuously since independence. (references) | |
Political Rights | Botswana | Members of the BDP have held a majority of seats in the National Assembly, and as a result also the presidency, continuously since independence. (references) |
Malaysia | National elections are required at least every 5 years and have been held regularly since independence in 1957. The Malay-based United Malay National Organization party dominates the ruling National Front coalition, which has ruled the country continuously since independence. (references) | |
Singapore | Opposition parties are free to contest elections, and the voting and vote-counting systems are fair and free from tampering; however, the PAP, which has held power continuously and overwhelmingly for more than 3 decades, uses the Government's extensive powers to place formidable obstacles in the path of political opponents. (references) | |
Trade | Brazil | Depending on the product, the registration may be valid from two to five years and can be renewed continuously for the same period. (references) |
Kenya | As the list of prohibited imports is continuously changing, importing firms should always check with the Kenyan Customs Department, Ministry of Finance, P.O. Box 30007, Nairobi, Kenya, Fax: 254-2-718-417, Tel: 254-2-715-540. (references) | |
Travel | Kenya | While there are numerous factors that may interfere with prompt shipment, the U.S. exporter should allow for additional shipping time to Kenya and ensure the Kenyan buyer is continuously updated on changes in the shipping schedules and routing. (references) |
Worker Rights | Belize | An employee is eligible for severance pay provided that he was employed continuously for at least 5 years. (references) |
Egypt | Children may not work overtime, during their weekly day off, between 8 p.m. and 7 a.m., or for more than 4 hours continuously. (references) | |
Zimbabwe | Minimum wages in the formal sector changed continuously as a result of multiple increases in salaries to offset the high inflation rate. (references) | |
Source: compiled by the editor from ICON Group International, Inc.; see credits. | ||
| "Continuously" is generally used as an adverb (general) -- approximately 100.00% of the time. "Continuously" is used about 888 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 |
| Adverb (general) | 100% | 888 | 8,019 |
Source: compiled by the editor from several corpora; see credits.
Expressions using "continuously": continuously computed release point ♦ continuously moving form ♦ continuously set vector ♦ weep continuously. Additional references. | |
| Hyphenated Usage | |
Beginning with "continuously": continuously-published, continuously-variable. | |
| 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 "continuously"; alternative meanings/domain in parentheses. | |
Afrikaans | permanent (abiding, constant, constantly, continual, continually, continuous, lasting, permanent, sustained), aldeur (all, all the time, ceaselessly, constantly, continually). (various references) | |
Albanian | vazhdimisht (again and again, ceaselessly, constantly, continually, incessantly, non-stop, repeatedly, unceasingly, uninterruptedly). (various references) | |
Arabic | باطراد. (various references) | |
Catalan | sempre (constantly, continually). (various references) | |
Chinese | 连续 (Continual, Continuance, Continuous, sequential, serial, succession, successive), 不住 (constantly, repeatedly), 一直 (all along, always, from the beginning of ... up to ...). (various references) | |
Czech | stále (all the time, always, constantly, incessantly, invariably, nonstop, non-stop, persistently, steadily, still), neustále (constantly, incessantly, perpetually), nepřetržitì (constantly, nonstop, non-stop, steadily). (various references) | |
Danish | COLT (Continuously Offered Longer-Term Securities(COLTS)), tjenester,der forbruges kollektivt indirekte og til stadighed (indirectly and continuously, services consumed collectively), strengstoebt emne (continuously cast slab), luftproever udtaget ved hjaelp af PVC-roer, er blevet analyseret enten kontinuerligt i et infraroedt spektroskop, eller enkeltvis ad kolorimetrisk vej (samples were taken of the atmosphere using P.V.C. piping and were analysed either continuously by an infra-red apparatus or discontinuously by means of colorimetric tubes), lange værdipapirer i løbende udbud (Continuously Offered Longer-Term Securities(COLTS)), kontinuerligt exciteret laser (continuously excited laser), kontinuerligt beregnet våbenafleveringspunkt (continuously computed release point), kontinuerligt armeret beton (continually reinforced concrete, continuously reinforced concrete), kontinuerlig vektoropdatering i bombesigtesystem (continuously set vector), bloed linjefoering (continuously flowing alignment). (various references) | |
Dutch | permanent (constantly, continually, perennial, permanent), aldoor (all the time, ceaselessly, constantly, continually). (various references) | |
Esperanto | daŭre (constantly, continually). (various references) | |
Finnish | yhtenään (constantly), yhtäjaksoisesti (without a break), lakkaamatta (ceaselessly, without intermission, without stopping), jatkuvasti (continually, without interruption). (various references) | |
French | continuellement (constantly, continually). (various references) | |
Frisian | aloan (all the time, ceaselessly, constantly, continually), algeduerigen (all the time, ceaselessly, constantly, continually). (various references) | |
German | fortlaufende (consecutive), fortgesetzt (continually, continued, continuing). (various references) | |
Greek | συνεχώσ (consecutively, constantly, continually), αδιάκοπα (ceaselessly). (various references) | |
Hebrew | לבכין (weep continuously). (various references) | |
Hungarian | állandóan (constantly, continually, invariably, permanently, perpetually, standing joke, to visit). (various references) | |
Indonesian | derai (in droves). (various references) | |
Italian | continuamente (away, continually, ever, evermore, hourly, non-stop), incessante (ceaseless, continuous, everlasting, incessant, nonstop, restless, unabating, unceasing, unending, uninterrupted, unremitting, unresting). (various references) | |
Japanese Kanji | 間断 (constantly), 縷縷と (at great length, in minute detail, unbroken), 縷縷 (at great length, in minute detail, unbroken), 打っ通しに (all through, throughout, without a break), 引っ切り無し (continually, incessantly), 始終 (from beginning to end), 始終 (from beginning to end), 切り無し (always). (various references) | |
Japanese Katakana | きりなし (always), しじゅう (forty, fourfold, from beginning to end), ひっきりなし (continually, incessantly), ぶっとおしに (all through, throughout, without a break), かんだん (chat, constantly, heat and cold, idle talk, pleasant talk, quiet conversation, temperature), るると (at great length, in minute detail, unbroken), るる (at great length, in minute detail, unbroken). (various references) | |
Korean | 끊임없 (incessantly, Perpetually). (various references) | |
Manx | rea (clear, clear as water, easy of manner, facile, flat, horizontal, level, male sheep, plain, plane, ram, regularly, sleek, smooth, steady, tup; even). (various references) | |
Pig Latin | ontinuouslycay.(various references) | |
Portuguese | continuamente (around-the-clock, ceaselessly, constantly, continually, day-and-night, hourly, night and day, round-the-clock). (various references) | |
Romanian | continuu (ceaseless, continual, continually, continuous, hourly, incessant, perpetual, running, sustained, unbroken, unceasing, uninterrupted, unremitting), mereu (again and again, all along, always, ceaselessly, constantly, continually, eternally, ever, ever after, invariably, permanently, right along, still). (various references) | |
Russian | непрерывно (permanently, right along, unceasingly, uninterruptedly). (various references) | |
Serbo-Croatian | stalno (constantly, continually, permanently, steadily), neprekidno (constantly, continually, end: on end, incessantly, seriatim). (various references) | |
Spanish | continuamente (all the time, ceaselessly, constantly, continually, incessantly, persistently), siempre (always, aye, constantly, continually, each time, ever, forever). (various references) | |
Swedish | oupphörligt (incessantly, night and day, without cease). (various references) | |
Turkish | sürekli olarak (continually, evermore, in ordinary, incessantly, invariably, on), durmadan (away, continual, continually, forever, night and day, non-stop, on, on and on, on end, repeatedly, without cease). (various references) | |
Ukrainian | безперервно (an-end, constantly), постійно (always, at every turn, ay, aye, constantly, frequently, invariably, permanently). (various references) | |
Vietnamese | liên tiếp (consecutive, continuous, reel), liên tục (cease, consecutive, continual, continuous, endless, reel, running, sequent, sequential, together, unceasing, unintermittent, unremitting). (various references) | |
| Source: compiled by the editor from various translation references. | ||
| Language | Period | Translations |
| Latin | 500 BCE-Modern | adsidue assidue, continuo, protinus, usque. (various references) |
| Source: compiled by the editor from various references. | ||
Derivations | |
Words ending with "continuously": discontinuously. (additional references) | |
| |
"Continuously" is suggested in spellcheckers for the following: contineously, continiously, continously, continueously, continuosly, contrinuously, countinuously. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "continuously" (pronounced kunti"nyuwuslē) |
| 7 | -n y uw u s l ē | strenuously. |
| 6 | -y uw u s l ē | conspicuously, unambiguously. |
| 5 | -uw u s l ē | incongruously. |
| 4 | -u s l ē | aimlessly, ambitiously, anonymously, anxiously, assiduously, autonomously, breathlessly, callously, capriciously, carelessly, cautiously, ceaselessly, conscientiously, consciously, contemporaneously, contemptuously, courageously, curiously, dangerously, deliciously, disastrously, jealously, judiciously, laboriously, effortlessly, egregiously, endlessly, enormously, enviously, erroneously, expeditiously, fabulously, facetiously, fallaciously, famously, ferociously, flawlessly, frivolously, fruitlessly, furiously, generously, gloriously, graciously, gratuitously, grievously, harmlessly, harmoniously, hellaciously, helplessly, hideously, hilariously, hopelessly, horrendously, humorously, indigenously, ingeniously, instantaneously, intravenously, listlessly, ludicrously, maliciously, marvelously, mercilessly, meticulously, mindlessly, miraculously, mysteriously, needlessly, nervously, notoriously, obviously, ominously, ostentatiously, outrageously, painlessly, perilously, piously, posthumously, precariously, precipitously, previously, prodigiously, purposely, recklessly, relentlessly, religiously, restlessly, ridiculously, righteously, rigorously, ruthlessly, scrupulously, seamlessly, seriously, shamelessly, simultaneously, spontaneously, studiously, subconsciously, surreptitiously, suspiciously, synonymously, tediously, tenaciously, tirelessly, tremendously, tremulously, unanimously, unceremoniously, unconsciously, variously, vicariously, viciously, vigorously, vociferously, zealously. |
| 3 | -s l ē | adversely, closely, concisely, conversely, densely, expressly, falsely, fiercely, grossly, immensely, intensely, inversely, loosely, nicely, parsley, perversely, precisely, princely, profusely, scarcely, sparsely, tensely, tersely, thusly. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "c-i-l-n-n-o-o-s-t-u-u-y" | |
-1 letter: innocuously. | |
-2 letters: continuous. | |
-3 letters: continuos, contusion, innocuous, locutions, nocuously. | |
-4 letters: colonist, continuo, cousinly, linocuts, locution, snootily, solution, stolonic, syntonic, unctions. | |
-5 letters: colonus, consult, cytosol, linocut, lotions, nocuous, nonoily, nonsuit, notions, nuncios, oculist, soliton, sootily, stonily, suction, sunnily, tycoons, tylosin, uncinus, uncoils, unction, unnoisy, unsoncy. | |
| Words containing the letters "c-i-l-n-n-o-o-s-t-u-u-y" | |
+3 letters: 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: Commercial | 5. Images: Photo Album 6. Images: Digital Art 7. Quotations: Familiar 8. Quotations: Fiction | 9. Quotations: Non-fiction 10. Usage Frequency 11. Expressions 12. Expressions: Internet | 13. Translations: Modern 14. Translations: Ancient 15. Abbreviations 16. Acronyms | 17. Derivations 18. Rhymes 19. Anagrams 20. Bibliography |
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