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transitive
     1. adj. Making a transit or passage.
     2. adj. Affected by transference of signification.
     3. adj. (grammar, of a verb) Taking an object or objects.
           The English verb "to notice" is a transitive verb, because we say things like "She noticeda problem".
     4. adj. (set theory, of a relation on a set) Having the property that if an element x is related to y and y is related to z, then x is necessarily related to z.
           "Is an ancestor of" is a transitive relation: if Alice is an ancestor of Bob, and Bob is an ancestor of Carol, then Alice is an ancestor of Carol.
     5. adj. (algebra, of a group action) Such that, for any two elements of the acted-upon set, some group element maps the first to the second.
     6. adj. (graph theory, of a graph) Such that, for any two vertices there exists an automorphism which maps one to the other.
Mathematics
     1. n. (alt-form, mathematics), especially when defined as a school subject.
     2. n. An abstract representational system used in the study of numbers, shapes, structure, change and the relationships between these concepts.
     3. n. A person's ability to count, calculate, and use different systems of mathematics at differing levels.
           My mathematics is always improving.
to
     1. part. A particle used for marking the following verb as an infinitive.
           I want to leave.
           He asked me what to do.
           I don’t know how to say it.
           I have places to go and people to see.
     2. part. As above, with the verb implied.
           "Did you visit the museum?" "I wanted to, but it was closed.".
           If he hasn't read it yet, he ought to.
     3. part. A particle used to create phrasal verbs.
           I have to do laundry today.
     4. prep. Indicating destination: In the direction of, and arriving at.
           We are walking to the shop.
     5. prep. Used to indicate purpose.
           He devoted himself to education.
           They drank to his health.
     6. prep. Used to indicate result of action.
           His face was beaten to a pulp.
     7. prep. Used after an adjective to indicate its application.
           similar to ..., relevant to ..., pertinent to ..., I was nice to him, he was cruel to her, I am used to walking.
     8. prep. (obsolete,) As a.
           With God to friend (with God as a friend);   with The Devil to fiend (with the Devil as a foe);   lambs slaughtered to lake (lambs slaughtered as a sacrifice);   t
     9. prep. (arithmetic) Used to indicate a ratio or comparison.
           one to one = 1:1
           ten to one = 10:1.
           I have ten dollars to your four.
     10. prep. (arithmetic) Used to indicate that the preceding term is to be raised to the power of the following value; indicates exponentiation.
           Three squared or three to the second power is nine.
           Three to the power of two is nine.
           Three to the second is nine.
     11. prep. Used to indicate the indirect object.
           I gave the book to him.
     12. prep. (time) Preceding.
           ten to ten = 9:50; We're going to leave at ten to (the hour).
     13. prep. Used to describe what something consists of or contains.
           Anyone could do this job; there's nothing to it.
           There's a lot of sense to what he says.
     14. prep. (Canada, UK, Newfoundland, West Midlands) At.
           Stay where you're to and I'll come find you, b'y.
     15. adv. Toward a closed, touching or engaging position.
           Please push the door to.
     16. adv. (nautical) Into the wind.
     17. adv. misspelling of too
combine
     1. v. To bring (two or more things or activities) together; to unite.
           Combine the milk and the hot water in a large bowl.   I'm combining business and pleasure on this trip.
     2. v. To have two or more things or properties that function together.
           Joe combines the intelligence of a rock with the honesty of a politician.
     3. v. (intransitive) To come together; to unite.
           two substances that easily combine
     4. v. (card games) In the game of casino, to play a card which will take two or more cards whose aggregate number of pips equals those of the card played.
     5. v. (obsolete) To bind; to hold by a moral tie.
     6. n. A combine harvester
           We can't finish harvesting because our combine is stuck in the mud.
     7. n. A combination
     8. n.          Especially, a joint enterprise of whatever legal form for a purpose of business or in any way promoting the interests of the participants, sometimes wi
                    The telecom companies were accused of having formed an illegal combine in order to hike up the network charges.
     9. n.          An industrial conglomeration in a socialist country, particularly in the former Soviet bloc.
free
     1. adj. (social) Unconstrained.
           He was given free rein to do whatever he wanted.
     2. adj.          Not imprisoned or enslaved.
                   a free man
     3. adj.          Unconstrained by timidity or distrust
     4. adj.          Generous; liberal.
                   He's very free with his money.
     5. adj.          (obsolete) Clear of offence or crime; guiltless; innocent.
     6. adj.          Without obligations.
                   free time
     7. adj.          Thrown open, or made accessible, to all; to be enjoyed without limitations; unrestricted; not obstructed, engrossed, or appropriated; open; said of a t
                   a free school
     8. adj.          Not arbitrary or despotic; assuring liberty; defending individual rights against encroachment by any person or class; instituted by a free people; said
                   This is a free country.
     9. adj.          (software) With no or only freedom-preserving limitations on distribution or modification.
                   OpenOffice is free software.
     10. adj.          (software) Intended for release, as opposed to a checked version.
     11. adj. Obtainable without any payment.
           The government provides free health care.
     12. adj.          (by extension, chiefly advertising slang) complimentary
                   Buy a TV to get a free DVD player!
     13. adj. (abstract) Unconstrained.
     14. adj.          (mathematics) Unconstrained by relators.
                   the free group on three generators
     15. adj.          (mathematics, logic) Unconstrained by quantifiers.
                   z is the free variable in\forall x\exists y:xy=z.
     16. adj.          (programming) Unconstrained of identifiers, not bound.
     17. adj.          (linguistics) (of a morpheme) That can be used by itself, unattached to another morpheme.
     18. adj. (physical) Unconstrained.
     19. adj.          Unobstructed, without blockages.
                   the drain was free
     20. adj.          Unattached or uncombined.
                   a free radical
     21. adj.          Not currently in use; not taken; unoccupied.
                   You can sit on this chair; it's free.
     22. adj.          (botany, mycology) Not attached; loose.
                   In this group of mushrooms, the gills are free.
     23. adj. Without; not containing (what is specified); exempt; clear; liberated.
           We had a wholesome, filling meal, free of meat.  I would like to live free from care in the mountains.
     24. adj. (dated) Ready; eager; acting without spurring or whipping; spirited.
           a free horse
     25. adj. (dated) Invested with a particular freedom or franchise; enjoying certain immunities or privileges; admitted to special rights; followed by of.
     26. adj. (legal) Certain or honourable; the opposite of base.
           free service;  free socage
     27. adj. (legal) Privileged or individual; the opposite of common.
           a free fishery;  a free warren
     28. adv. Without needing to pay.
           I got this bike free.
     29. adv. (obsolete) Freely; willingly.
     30. v. To make free; set at liberty; release; rid of that which confines, limits, embarrasses, or oppresses.
     31. n. (Australian rules football, Gaelic football) (abbreviation of free kick).
     32. n. free transfer
     33. n. (hurling) The usual means of restarting play after a foul is committed, where the non-offending team restarts from where the foul was committed.
groups
     1. n. plural of group
     2. v. third-person singular present indicative of group
by
     1. prep. Near or next to.
           The mailbox is by the bus stop.
     2. prep. At some time before (the given time), or before the end of a given time interval.
           Be back by ten o'clock!  We will send it by the first week of July.
     3. prep. Indicates the actor in a clause with its verb in the passive voice: Through the action or presence of.
           The matter was decided by the chairman.  The boat was swamped by the water.  He was protected by his body armour.
     4. prep. Indicates the creator of a work: Existing through the authorship etc. of.
           There are many well-known plays by William Shakespeare
     5. prep. Indicates the cause of a condition or event: Through the action of, caused by, responsibility for; by dint of.
     6. prep. Indicates a means: Involving/using the means of.
           I avoided the guards by moving only when they weren't looking.
     7. prep. Indicates a source of light used as illumination.
           The electricity was cut off, so we had to read by candlelight.
     8. prep. Indicates an authority, rule, or permission followed.
           I sorted the items by category.  By the power vested in me, I now pronounce you man and wife.
     9. prep. Indicates the amount of some progression: With a change of.
           Our stock is up by ten percent.
     10. prep. In the formulae X by X and by Xs, indicates a steady progression, one X after another.
           We went through the book page by page.  We crawled forward by inches.
     11. prep. Indicates a referenced source: According to.
           He cheated by his own admission.
     12. prep. Indicates an oath: With the authority of.
           By Jove! I think she's got it!  By all that is holy, I'll put an end to this.
     13. prep. Used to separate dimensions when describing the size of something.
           It is easy to invert a 2-by-2 matrix.  The room was about 4 foot by 6 foot.  The bricks used to build the wall measured 10 by 20 by 30 cm.
     14. prep. (horse breeding) Designates a horse's male parent (sire); cf. out of.
           She's a lovely little filly, by Big Lad, out of Damsel in Distress.
     15. adv. Along a path which runs by the speaker.
           I watched as it passed by.
     16. adv. In the vicinity, near.
           There was a shepherd close by.
           The shop is hard by the High Street.
     17. adv. To or at a place, as a residence or place of business.
           I'll stop by on my way home from work.
           We're right near the lifeguard station. Come by before you leave.
     18. adv. Aside, away.
           The women spent much time after harvest putting jams by for winter and spring.
     19. adj. Out of the way, subsidiary.
     20. n. (card games) A pass
     21. interj. alternative spelling of bye
identifying
     1. v. present participle of identify
     2. n. An act of identification.
     identify
          1. v. To establish the identity of someone or something.
          2. v. (transitive, biology) To establish the taxonomic classification of an organism.
          3. v. To equate or make the same; to unite or combine into one.
          4. v. (reflexive) To have a strong affinity with; to feel oneself to be modelled on or connected to.
          5. v. (intransitive) To associate oneself with some group.
          6. v. (intransitive) To claim an identity; to describe oneself as a member of a group; to assert the use of a particular term to describe oneself.
respective
     1. adj. Relating to particular persons or things, each to each; particular; own.
           They returned to their respective places of abode.
     2. adj. (obsolete) Noticing with attention; careful; wary.
     3. adj. (obsolete) Looking toward; having reference to; relative, not absolute.
           the respective connections of society
     4. adj. (obsolete) Fitted to awaken respect.
     5. adj. (obsolete) Rendering respect; respectful; regardful.
isomorphic
     1. adj. (mathematics) Related by an isomorphism; having a structure-preserving one-to-one correspondence.
     2. adj. (biology) Having a similar structure or function to something that is not related genetically or through evolution.
     3. adj. Having identical relevant structure; being structure-preserving while undergoing certain invertible transformations.
subgroups
     1. n. plural of subgroup
Dictionary entries from Wiktionary