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graph
     1. n. (applied mathematics, statistics) A data chart (graphical representation of data) intended to illustrate the relationship between a set (or sets) of numbers (quantities, measurements or indicative num
     2. n. (mathematics) A set of points constituting a graphical representation of a real function; (formally) a set of tuples(x_1, x_2, \ldots, x_m, y)\in\R^m+1, wherey=f(x_1, x_2, \ldots, x_m) for a given fun
     3. n. (graph theory) (formally) An ordered pair of sets(V,E), where the elements ofV are called vertices or nodes andE is a set of pairs (called edges) of elements ofV; (less formally) a set of vertices (or
     4. n. (topology) A topological space which represents some graph (ordered pair of sets) and which is constructed by representing the vertices as points and the edges as copies of the real interval 0,1 (wher
     5. n. (category theory, of a morphism f) A morphism\Gamma_f from the domain off to the product of the domain and codomain off, such that the first projection applied to\Gamma_f equals the identity of the do
     6. n. (linguistics, typography) A graphical unit on the token-level, the abstracted fundamental shape of a character or letter as distinct from its ductus (realization in a particular typeface or handwritin
     7. v. To draw a graph.
     8. v. (transitive, mathematics) To draw a graph of a function.
theory
     1. n. An description of an event or system that is considered to be accurate.
     2. n. (obsolete) Mental conception; reflection, consideration.
     3. n. (sciences) A coherent statement or set of ideas that explains observed facts or phenomena and correctly predicts new facts or phenomena not previously observed, or which sets out the laws and principl
     4. n. The underlying principles or methods of a given technical skill, art etc., as opposed to its practice.
     5. n. (mathematics) A field of study attempting to exhaustively describe a particular class of constructs.
           Knot theory classifies the mappings of a circle into 3-space.
     6. n. A hypothesis or conjecture.
     7. n. (logic) A set of axioms together with all statements derivable from them; or, a set of statements which are deductively closed. Equivalently, a formal language plus a set of axioms (from which can the
           A theory is consistent if it has a model.
the
     1. art. Definite grammatical article that implies necessarily that an entity it articulates is presupposed; something already mentioned, or completely specified later in that same sentence, or assumed already
           I’m reading the book. (Compare I’m reading a book.)
           The street in front of your house. (Compare A street in Paris.)
           The men and women watched the man give the birdseed to the bird.
     2. art.          Used before a noun modified by a restrictive relative clause, indicating that the noun refers to a single referent defined by the relative clause.
                    The street that runs through my hometown.
     3. art. Used before an object considered to be unique, or of which there is only one at a time.
           No one knows how many galaxies there are in the universe.
           God save the Queen!
     4. art. Used before a superlative or an ordinal number modifying a noun, to indicate that the noun refers to a single item.
           That was the best apple pie ever.
     5. art.          Added to a superlative or an ordinal number to make it into a substantive.
                    That apple pie was the best.
     6. art. Introducing a singular term to be taken generically: preceding a name of something standing for a whole class.
     7. art. Used before an adjective, indicating all things (especially persons) described by that adjective.
           Feed the hungry, clothe the naked, comfort the afflicted, and afflict the comfortable.
     8. art. Used to indicate a certain example of (a noun) which is usually of most concern or most common or familiar.
           No one in the whole country had seen it before.
           I don't think I'll get to it until the morning.
     9. art. Used before a body part (especially of someone previously mentioned), as an alternative to a possessive pronoun.
           A stone hit him on the head. (= “A stone hit him on his head.”)
     10. art. When stressed, indicates that it describes an object which is considered to be best or exclusively worthy of attention.
           That is the hospital to go to for heart surgery.
     11. adv. 1=With a comparative ormore and a verb phrase, establishes a parallel with one or more other such comparatives.
           The hotter the better.
           The more I think about it, the weaker it looks.
           The more money donated, the more books purchased, and the more happy children.
           It looks weaker and weaker, the more I think about it.
     12. adv. 1=With a comparative, and often withfor it, indicates a result more like said comparative. This can be negated withnone.
           It was a difficult time, but I’m the wiser for it.
           It was a difficult time, and I’m none the wiser for it.
           I'm much the wiser for having had a difficult time like that.
length
     1. n. The distance measured along the longest dimension of an object.
     2. n. Duration.
     3. n. (horse racing) The length of a horse, used to indicate the distance between horses at the end of a race.
     4. n. (mathematics) Distance between the two ends of a line segment.
     5. n. (cricket) The distance down the pitch that the ball bounces on its way to the batsman.
     6. n. (figuratively) Total extent.
           the length of a book
     7. n. Part of something that is long; a physical piece of something.
           a length of rope
     8. v. (obsolete) To lengthen.
of
     1. prep. Expressing distance or motion.
     2. prep.          (now obsolete, or dialectal) From (of distance, direction), "off".
     3. prep.          (obsolete except in phrases) Since, from (a given time, earlier state etc.).
     4. prep.          From, away from (a position, number, distance etc.).
                    There are no shops within twenty miles of the cottage.
     5. prep.          (North America, Scotland, Ireland) Before (the hour); to.
                    What's the time? / Nearly a quarter of three.
     6. prep. Expressing separation.
     7. prep.          (Indicating removal, absence or separation, with the action indicated by a transitive verb and the quality or substance by a grammatical object.)
                    Finally she was relieved of the burden of caring for her sick husband.
     8. prep.          (Indicating removal, absence or separation, with resulting state indicated by an adjective.)
                    He seemed devoid of human feelings.
     9. prep.          (obsolete) (Indicating removal, absence or separation, construed with an intransitive verb.)
     10. prep. Expressing origin.
     11. prep.          (Indicating an ancestral source or origin of descent.)
                    The word is believed to be of Japanese origin.
     12. prep.          (Indicating a (non-physical) source of action or emotion; introducing a cause, instigation); from, out of, as an expression of.
                    The invention was born of necessity.
     13. prep.          (following an intransitive verb) (Indicates the source or cause of the verb.)
                    It is said that she died of a broken heart.
     14. prep.          (following an adjective) (Indicates the subject or cause of the adjective.)
                    I am tired of all this nonsense.
     15. prep. Expressing agency.
     16. prep.          (following a passive verb) (Indicates the agent (for most verbs, now usually expressed with by).)
                    I am not particularly enamoured of this idea.
     17. prep.          (Used to introduce the "subjective genitive"; following a noun to form the head of a postmodifying noun phrase) (see also 'Possession' senses below).
                    The contract can be terminated at any time with the agreement of both parties.
     18. prep.          (following an adjective) (Used to indicate the agent of something described by the adjective.)
                    It was very brave of you to speak out like that.
     19. prep. Expressing composition, substance.
     20. prep.          (after a verb expressing construction, making etc.) (Used to indicate the material or substance used.)
                    Many 'corks' are now actually made of plastic.
     21. prep.          (directly following a noun) (Used to indicate the material of the just-mentioned object.)
                    She wore a dress of silk.
     22. prep.          (Indicating the composition of a given collective or quantitative noun.)
                    What a lot of nonsense!
     23. prep.          (Used to link a given class of things with a specific example of that class.)
                   Welcome to the historic town of Harwich.
     24. prep.          (Links two nouns in near-apposition, with the first qualifying the second); "which is also".
                    I'm not driving this wreck of a car.
     25. prep. Introducing subject matter.
     26. prep.          (Links an intransitive verb, or a transitive verb and its subject (especially verbs to do with thinking, feeling, expressing etc.), with its subject-ma
                    I'm always thinking of you.
     27. prep.          (following a noun (now chiefly nouns of knowledge, communication etc.)) (Introduces its subject matter); about, concerning.
                    He told us the story of his journey to India.
     28. prep.          (following an adjective) (Introduces its subject matter.)
                    This behaviour is typical of teenagers.
     29. prep. Having partitive effect.
     30. prep.          (following a number or other quantitive word) (Introduces the whole for which is indicated only the specified part or segment); "from among".
                    Most of these apples are rotten.
     31. prep.          (following a noun) (Indicates a given part.)
     32. prep.          (now archaic, literary, with preceding partitive word assumed, or as a predicate after to be) Some, an amount of, one of.
                    On the whole, they seem to be of the decent sort.
     33. prep.          (Links to a genitive noun or possessive pronoun, with partitive effect (though now often merged with possessive senses, below).)
                    He is a friend of mine.
     34. prep. Expressing possession.
     35. prep.          Belonging to, existing in, or taking place in a given location, place or time. Compare "origin" senses, above.
                    He was perhaps the most famous scientist of the twentieth century.
     36. prep.          Belonging to (a place) through having title, ownership or control over it.
                    The owner of the nightclub was arrested.
     37. prep.          Belonging to (someone or something) as something they possess or have as a characteristic; (the "possessive genitive". (With abstract nouns, this inter
                    Keep the handle of the saucepan away from the flames.
     38. prep. Forming the "objective genitive".
     39. prep.          (Follows an agent noun, verbal noun or noun of action.)
                    She had a profound distrust of the police.
     40. prep. Expressing qualities or characteristics.
     41. prep.          (now archaic, or literary) (Links an adjective with a noun or noun phrase to form a quasi-adverbial qualifier); in respect to, as regards.
                    My companion seemed affable and easy of manner.
     42. prep.          (Indicates a quality or characteristic); "characterized by".
                    Pooh was said to be a bear of very little brain.
     43. prep.          (Indicates quantity, age, price, etc.)
                    We have been paying interest at a rate of 10%.
     44. prep.          (US, informal considered incorrect by some) (Used to link singular indefinite nouns (preceded by the indefinite article) and attributive adjectives mod
                    It's not that big of a deal.
     45. prep. Expressing a point in time.
     46. prep.          (chiefly regional) During the course of (a set period of time, day of the week etc.), now specifically with implied repetition or regularity.
                    Of an evening, we would often go for a stroll along the river.
     47. prep.          (UK dialectal, chiefly in negative constructions) For (a given length of time).
                    I've not tekken her out of a goodly long while.
     48. prep.          (after a noun) (Indicates duration of a state, activity etc.)
                    After a delay of three hours, the plane finally took off.
the
     1. art. Definite grammatical article that implies necessarily that an entity it articulates is presupposed; something already mentioned, or completely specified later in that same sentence, or assumed already
           I’m reading the book. (Compare I’m reading a book.)
           The street in front of your house. (Compare A street in Paris.)
           The men and women watched the man give the birdseed to the bird.
     2. art.          Used before a noun modified by a restrictive relative clause, indicating that the noun refers to a single referent defined by the relative clause.
                    The street that runs through my hometown.
     3. art. Used before an object considered to be unique, or of which there is only one at a time.
           No one knows how many galaxies there are in the universe.
           God save the Queen!
     4. art. Used before a superlative or an ordinal number modifying a noun, to indicate that the noun refers to a single item.
           That was the best apple pie ever.
     5. art.          Added to a superlative or an ordinal number to make it into a substantive.
                    That apple pie was the best.
     6. art. Introducing a singular term to be taken generically: preceding a name of something standing for a whole class.
     7. art. Used before an adjective, indicating all things (especially persons) described by that adjective.
           Feed the hungry, clothe the naked, comfort the afflicted, and afflict the comfortable.
     8. art. Used to indicate a certain example of (a noun) which is usually of most concern or most common or familiar.
           No one in the whole country had seen it before.
           I don't think I'll get to it until the morning.
     9. art. Used before a body part (especially of someone previously mentioned), as an alternative to a possessive pronoun.
           A stone hit him on the head. (= “A stone hit him on his head.”)
     10. art. When stressed, indicates that it describes an object which is considered to be best or exclusively worthy of attention.
           That is the hospital to go to for heart surgery.
     11. adv. 1=With a comparative ormore and a verb phrase, establishes a parallel with one or more other such comparatives.
           The hotter the better.
           The more I think about it, the weaker it looks.
           The more money donated, the more books purchased, and the more happy children.
           It looks weaker and weaker, the more I think about it.
     12. adv. 1=With a comparative, and often withfor it, indicates a result more like said comparative. This can be negated withnone.
           It was a difficult time, but I’m the wiser for it.
           It was a difficult time, and I’m none the wiser for it.
           I'm much the wiser for having had a difficult time like that.
shortest
     1. adj. superlative form of short: most short; Least in stature, length or height.
           The two-word poem "Fleas", by Ogden Nash, is arguably the shortest poem in the English language.
cycle
     1. n. An interval of space or time in which one set of events or phenomena is completed.
           the cycle of the seasons, or of the year
     2. n. A complete rotation of anything.
     3. n. A process that returns to its beginning and then repeats itself in the same sequence.
     4. n. The members of the sequence formed by such a process.
     5. n. (music) In musical set theory, an interval cycle is the set of pitch classes resulting from repeatedly applying the same interval class to the starting pitch class.
           The interval cycle C4 consists of the pitch classes 0, 4 and 8; when starting on E, it is realised as the pitches E, Gand C.
     6. n. A series of poems, songs or other works of art.
           The "Ring of the Nibelung" is a cycle of four operas by Richard Wagner, the famous nineteenth-century German composer.
     7. n. A programme on a washing machine, dishwasher, or other such device.
           Put the washing in on a warm cycle.
           the spin cycle
     8. n. A pedal-powered vehicle, such as a unicycle, bicycle, or tricycle, or a motorized vehicle that has either two or three wheels, such as a motorbike, motorcycle, motorized tricycle, or motortrike.
     9. n. (baseball) A single, a double, a triple, and a home run hit by the same player in the same game.
           Jones hit for the cycle in the game.
     10. n. (graph theory) A closed walk or path, with or without repeated vertices allowed.
     11. n. (topology, algebraic topology) A chain whose boundary is zero.
     12. n. An imaginary circle or orbit in the heavens; one of the celestial spheres.
     13. n. An age; a long period of time.
     14. n. An orderly list for a given time; a calendar.
     15. n. (botany) One entire round in a circle or a spire.
           a cycle or set of leaves
     16. v. To ride a bicycle or other cycle.
     17. v. To go through a cycle or to put through a cycle.
     18. v. (electronics) To turn power off and back on
           Avoid cycling the device unnecessarily.
     19. v. (ice hockey) To maintain a team's possession of the puck in the offensive zone by handling and passing the puck in a loop from the boards near the goal up the side boards and passing to back to the bo
           They have their cycling game going tonight.
in
     1. prep. Used to indicate location, inclusion, or position within spatial, temporal or other limits.
     2. prep.          Contained by.
                   The dog is in the kennel.
     3. prep.          Within.
     4. prep.          Surrounded by.
                   We are in the enemy camp.   Her plane is in the air.
     5. prep.          Part of; a member of.
                   One in a million.   She's in band and orchestra.
     6. prep.          Pertaining to; with regard to.
                   What grade did he get in English?
                   Military letters should be formal in tone, but not stilted.
     7. prep.          At the end of a period of time.
                   They said they would call us in a week.
     8. prep.          Within a certain elapsed time
                   Are you able to finish this in three hours?   The massacre resulted in over 1000 deaths in three hours.
     9. prep.          During (said of periods of time).
                   in the first week of December;  Easter falls in the fourth lunar month;   The country reached a high level of prosperity in his fi
     10. prep.          (grammar, phonetics, of sounds and letters) Coming at the end of a word.
                   English nouns in -ce form their plurals in -s.
     11. prep. Into.
           Less water gets in your boots this way.
     12. prep. Used to indicate limit, qualification, condition, or circumstance.
           In replacing the faucet washers, he felt he was making his contribution to the environment.
     13. prep.          Indicating an order or arrangement.
                   My fat rolls around in folds.
     14. prep.          Denoting a state of the subject.
                   He stalked away in anger.   John is in a coma.
     15. prep.          Indicates, connotatively, a place-like form of someone's (or something's) personality, as his, her or its psychic and physical characteristics.
                   You've got a friend in me.   He's met his match in her.
     16. prep.          Wearing (an item of clothing).
                    I glanced over at the pretty girl in the red dress.
     17. prep. Used to indicate means, medium, format, genre, or instrumentality.
     18. prep.          (of something offered or given in an exchange) In the form of, in the denomination of.
                   Please pay me in cash — preferably in tens and twenties.
                   The deposit can be in any legal tender, even in gold.
                    Her generosity was rewarded in the success of its recipients.
     19. prep.          Used to indicate a language, script, tone, etc. of a text, speech, etc.
                   Beethoven's "Symphony No. 5" in C minor is among his most popular.
                   His speech was in French, but was simultaneously translated into eight languages.
                   When you write in cursive, it's illegible.
     20. v. (obsolete, transitive) To enclose.
     21. v. (obsolete, transitive) To take in; to harvest.
     22. adv. (not comparable) Located indoors, especially at home or the office, or inside something.
           Is Mr. Smith in?
     23. adv. Moving to the interior of a defined space, such as a building or room.
           Suddenly a strange man walked in.
     24. adv. (sports) Still eligible to play, e.g. able to bat in cricket and baseball.
           He went for the wild toss but wasn't able to stay in.
     25. adv. (UK) Abbreviation of in aid of.
           What's that in?
     26. adv. After the beginning of something.
     27. n. A position of power or a way to get it.
           His parents got him an in with the company
     28. n. (sport) The state of a batter/batsman who is currently batting – see innings
     29. n. A re-entrant angle; a nook or corner.
     30. adj. In fashion; popular.
           Skirts are in this year.
     31. adj. Incoming.
           the in train
     32. adj. (nautical, of the sails of a vessel) Furled or stowed.
     33. adj. (legal) With privilege or possession; used to denote a holding, possession, or seisin.
           in by descent; in by purchase; in of the seisin of her husband
     34. adj. (cricket) Currently batting.
     35. n. Inch.
a
     1. art. One; any indefinite example of; used to denote a singular item of a group.
           There was a man here looking for you yesterday.
     2. art. Used in conjunction with the adjectives score, dozen, hundred, thousand, and million, as a function word.
           I've seen it happen a hundred times.
     3. art. One certain or particular; any single.Brown, Lesley, (2003)
           We've received an interesting letter from a Mrs. Miggins of London.
     4. art. The same; one.
           We are of a mind on matters of morals.
     5. art. Any, every; used before a noun which has become modified to limit its scope; also used with a negative to indicate not a single one.Lindberg, Christine A. (2007)
           A man who dies intestate leaves his children troubles and difficulties.
           He fell all that way, and hasn't a bump on his head?
     6. art. Used before plural nouns modified by few, good many, couple, great many, etc.
     7. art. Someone or something like; similar to; Used before a proper noun to create an example out of it.
           The center of the village was becoming a Times Square.
     8. prep. (archaic) To do with position or direction; In, on, at, by, towards, onto.
           Stand a tiptoe.
     9. prep. To do with separation; In, into.
           Torn a pieces.
     10. prep. To do with time; Each, per, in, on, by.
           I brush my teeth twice a day.
     11. prep. (obsolete) To do with method; In, with.
     12. prep. (obsolete) To do with role or capacity; In.
           A God’s name.
     13. prep. To do with status; In.
           King James Bible (II Chronicles 2:18)
             To set the people a worke.
     14. prep. (archaic) To do with process, with a passive verb; In the course of, experiencing.
           1964, Bob Dylan, The Times They Are a-Changin’
             The times, they are a-changin'.
     15. prep. (archaic) To do with an action, an active verb; Engaged in.
           1611, King James Bible, Hebrews 11-21
             Jacob, when he was a dying
     16. prep. (archaic) To do with an action/movement; To, into.
     17. v. (archaic, or slang) Have.
           I'd a come, if you'd a asked.
     18. pron. (obsolete, outside, England, and Scotland dialects) He.
     19. interj. A meaningless syllable; ah.
     20. prep. (archaic, slang) Of.
           The name of John a Gaunt.
     21. adv. (chiefly Scotland) All.
     22. adj. (chiefly Scotland) All.
graph
     1. n. (applied mathematics, statistics) A data chart (graphical representation of data) intended to illustrate the relationship between a set (or sets) of numbers (quantities, measurements or indicative num
     2. n. (mathematics) A set of points constituting a graphical representation of a real function; (formally) a set of tuples(x_1, x_2, \ldots, x_m, y)\in\R^m+1, wherey=f(x_1, x_2, \ldots, x_m) for a given fun
     3. n. (graph theory) (formally) An ordered pair of sets(V,E), where the elements ofV are called vertices or nodes andE is a set of pairs (called edges) of elements ofV; (less formally) a set of vertices (or
     4. n. (topology) A topological space which represents some graph (ordered pair of sets) and which is constructed by representing the vertices as points and the edges as copies of the real interval 0,1 (wher
     5. n. (category theory, of a morphism f) A morphism\Gamma_f from the domain off to the product of the domain and codomain off, such that the first projection applied to\Gamma_f equals the identity of the do
     6. n. (linguistics, typography) A graphical unit on the token-level, the abstracted fundamental shape of a character or letter as distinct from its ductus (realization in a particular typeface or handwritin
     7. v. To draw a graph.
     8. v. (transitive, mathematics) To draw a graph of a function.
Dictionary entries from Wiktionary