Vocabulary

  • in fact: Used to emphasize the truth of a statement, especially one that contrasts with or contradicts something else.
  • got to: To arrive at some place
  • look at: To use your eyes to focus on something
  • out of order: Not in proper working condition; broken.
  • have to: Must do
  • of course: Sure ; Certainly
  • at a time: Separately; one by one
  • in a row: One after another without a break.
  • for example: As an illustration or instance.
  • figure out: To understand the behavior of someone
  • from the start: From the very beginning; from the outset.
  • make some noise: To create a loud sound, often to show excitement or approval.
  • fit in: To mix with others so you get on well with them
  • hold in: To hide your emotions and not let them show
  • the following: Next in order or sequence.
  • think about: To consider something carefully.
  • in a while: In a short period of time; soon.
  • once in a while: Occasionally; not very often.
  • write down: To record in writing
  • talking about: To discuss a particular topic.
  • by example: Through demonstration or serving as a model.
  • at least: As a minimum
  • out there: In or to a place that is far away
  • in order to: For the purpose of; with the aim of.
  • with respect to: In relation to; regarding.
  • to let: Indicates that a property is available for rent.
  • used to: Did regularly before, but don't do now
  • back then: At that time in the past.
  • start over: To begin again.
  • up there: In or to a higher place or position; far away.
  • for free: Without charge; at no cost.
  • in mind: Being aware of or considering something.
  • going on: To continue doing something
  • to the point: Expressing something directly and without unnecessary detail.
  • in writing: Expressed or presented in written form, rather than spoken.
  • end up with: To have something as a result.
  • from top to bottom: Completely or thoroughly; in every part.
  • much about: A lot of information or knowledge concerning something.
  • to do with: To be about something; concern
  • take off: To remove, e.g. your clothes
  • up against: Facing or contending with something difficult or challenging.
  • funny business: Dishonest or suspicious activity.
  • run by: To be managed or controlled by someone or a group.
  • bring down: To destroy (government, etc.) forcefully
  • next to: Being located along side another
  • on a regular basis: Happening frequently or at regular intervals.
  • move on: To decide to change or go to a different place
  • for good measure: As an extra amount; in addition to what is strictly necessary.
  • goes well: To happen in the way desired
  • turned out: To arrive for a public event or entertainment
  • in the first place: To begin with; as the first point or consideration.
  • play around: To cheat on your partner romantically
  • look for: To try to find a thing or person that is lost
  • down with: Suffering from an illness.
  • draw out: To lengthen (far beyond the normal limits)
  • think of: To look on as (being something specific); consider
  • in on: To be involved in a secret or plan.
  • also known as: Also called; alternatively named.
  • know about: To have information or understanding of a subject or situation.
  • get here: To arrive at a specific location.
  • start on: To begin or start doing something.
  • as a result of: Because of something; owing to.
  • drop by: To visit someone or some place for a short time
  • one of each: A single item from every available type or variety.
  • order in: To request food from a restaurant to be delivered to one's home or other location.
  • as follows: Used to introduce a list or explanation.
  • one and the same: Exactly the same person or thing.
  • set up
  • move to: To change the place where you live or work.
  • after all: In spite of what was expected; used to introduce a statement that supports a previous statement or explains why it was made
  • in other words: Stating something in a different way, often to make it clearer or more understandable.
  • by now: At the present time or already; before the present.
  • move into: To start living in a new house or building
  • to the left: In or toward the left direction.
  • pin down: To force someone to clarify their opinion
  • in a state: In a particular condition or situation.
  • for the rest: Concerning the remaining people or things.
  • put together: To build or assemble something small, e.g. a toy
  • with it: Intelligent, alert, and up-to-date.
  • in a minute: Very soon; in a short amount of time.
  • of choice: Indicating something is preferred or selected deliberately.
  • pass out: To distribute or hand out papers to people
  • split up: To break up your marriage or relationship
  • one up: In a better or more advantageous position.
  • mess over: To treat someone unfairly or badly.
  • state: Region within a country, with its own government
  • audience: Group of people attending a play, movie etc.
  • good: Proper, appropriate or right
  • order: Religious or social group, as of nuns
  • odd: Being unmatched with someone or something
  • fact: Something that is known or proved to be true
  • number: Symbols such as 1, 2, 56, 793
  • prove: To demonstrate truth by providing evidence
  • row: To move a boat using oars
  • hypothesis: A theory trying to explain something
  • move: To cause someone to have certain emotions
  • score: A sharp mark or cut in the surface of something
  • proof: Act of showing that something exists or is true
  • column: Regular series of articles in a newspaper/magazine
  • class: To place things into groups by common qualities
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  • not found vocabularyNo vocabulary matches your filters
    • after all

      US /ˈæftɚ ɔl/

      UK /ˈɑ:ftə ɔ:l/

      • Adverb
      • In spite of what was expected; used to introduce a statement that supports a previous statement or explains why it was made
      • Considering everything; used to indicate that something is happening or is true despite some difficulty or obstacle
      • Phrase
      • Despite what was expected or thought; in spite of everything.
      • Taking everything into consideration; considering that.
      B1
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    • also known as

      US

      UK

      • Phrase
      • Also called; alternatively named.
      • Identified by another term; synonymous with.
      A1
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    • as a result of

      US

      UK

      • Phrase
      • Because of something; owing to.
      A1
      More
    • as follows

      US

      UK

      • Phrase
      • Used to introduce a list or explanation.
      A1
      More
    • at a time

      US /æt e taɪm/

      UK /æt ə taim/

      • Phrase
      • Separately; one by one
      • Simultaneously; together
      A1
      More
    • at least

      US /æt list/

      UK /æt li:st/

      • Adverb
      • As a minimum
      • Not less than
      • Phrase
      • No less than; at the minimum
      • Used to indicate that something is positive in a bad situation.
      C2
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    • audience

      US /ˈɔdiəns/

      UK /ˈɔ:diəns/

      • Noun (Countable/Uncountable)
      • Group of people attending a play, movie etc.
      A2TOEIC
      More
    • back then

      US

      UK

      • Phrase
      • At that time in the past.
      A1
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    • bring down

      US /brɪŋ daʊn/

      UK /briŋ daun/

      • Phrasal Verb
      • To destroy (government, etc.) forcefully
      • To kill someone, often with a gun
      A1
      More
    • by example

      US

      UK

      • Phrase
      • Through demonstration or serving as a model.
      • Through one's own behavior and actions, rather than just words.
      A2
      More
    • by now

      US /baɪ naʊ/

      UK /bai nau/

      • Phrase
      • At the present time or already; before the present.
      A2
      More
    • column

      US /ˈkɑ:ləm/

      UK /ˈkɒləm/

      • Noun (Countable/Uncountable)
      • Regular series of articles in a newspaper/magazine
      • Strong vertical stone pillar that holds up a roof
      B1
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    • down with

      US /daʊn wɪð/

      UK /daun wið/

      • Adjective
      • Suffering from an illness.
      • Agreeable to; in favor of.
      • Interjection
      • An expression of opposition to something.
      A1
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    • draw out

      US /drɔ aʊt/

      UK /drɔ: aut/

      • Phrasal Verb
      • To lengthen (far beyond the normal limits)
      • To get someone to tell you their real feelings
      A1
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    • drop by

      US /drɑp baɪ/

      UK /drɔp bai/

      • Phrasal Verb
      • To visit someone or some place for a short time
      A1
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    • end up with

      US

      UK

      • Phrasal Verb
      • To have something as a result.
      A1
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    • figure out

      US /ˈfɪɡjɚ aʊt/

      UK /ˈfiɡə aut/

      • Phrasal Verb
      • To understand the behavior of someone
      • To think through logically to find a solution
      • Verb (Transitive/Intransitive)
      • To understand or find an answer to something.
      • To find a solution to a problem or understand something.
      A1
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    • fit in

      US /fɪt ɪn/

      UK /fit in/

      • Phrasal Verb
      • To mix with others so you get on well with them
      A2
      More
    • for example

      US

      UK

      • Phrase
      • As an illustration or instance.
      More
    • for free

      US /fɔr fri/

      UK /fɔ: fri:/

      • Phrase
      • Without charge; at no cost.
      • Adjective
      • Available without payment.
      A2
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    • for good measure

      US

      UK

      • Idiom
      • As an extra amount; in addition to what is strictly necessary.
      • Phrase
      • As an extra amount; in addition to what is strictly necessary.
      More
    • for the rest

      US /fɔr ði rɛst/

      UK /fɔ: ðə rest/

      • Phrase
      • Concerning the remaining people or things.
      • During the remaining part of a period of time.
      A1
      More
    • from the start

      US /frʌm ði stɑrt/

      UK /frɔm ðə stɑ:t/

      • Phrase
      • From the very beginning; from the outset.
      A1
      More
    • from top to bottom

      US /frəm tɑp tu ˈbɑtəm/

      UK /frəm tɒp tə ˈbɒtəm/

      • other
      • Completely or thoroughly; in every part.
      B1
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    • funny business

      US

      UK

      • Noun (Countable/Uncountable)
      • Dishonest or suspicious activity.
      A1
      More
    • get here

      US

      UK

      • Intransitive Verb
      • To arrive at a specific location.
      A1
      More
    • goes well

      US

      UK

      • Phrasal Verb
      • To happen in the way desired
      • Intransitive Verb
      • To be successful or satisfactory; to turn out favorably.
      • To be harmonious or matching; to look good together.
      A1
      More
    • going on

      US /ˈɡoɪŋ ɑn/

      UK /ˈgəʊɪŋ ɔn/

      • Phrasal Verb
      • To continue doing something
      • To happen (usually negative)
      A1
      More
    • got to

      US /ɡɑt tu/

      UK /gɔt tu:/

      • Verb (Transitive/Intransitive)
      • To arrive at some place
      • To have the opportunity or permission to do something
      • Phrasal Verb
      • To appeal to the emotions of; move
      • To finally begin to start something after a delay
      A1
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    • have to

      US /hæv tu/

      UK /ˈhæv tə/

      • Auxiliary Verb
      • Must do
      A1
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    • hold in

      US /hold ɪn/

      UK /həuld in/

      • Phrasal Verb
      • To hide your emotions and not let them show
      A1
      More
    • hypothesis

      US /haɪˈpɑθɪsɪs/

      UK /haɪˈpɒθəsɪs/

      • Noun
      • A theory trying to explain something
      • A supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation.
      B1
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    • in a minute

      US

      UK

      • Phrase
      • Very soon; in a short amount of time.
      • Within the duration of one minute.
      A1
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    • in a row

      US /ɪn e ro/

      UK /in ə rəu/

      • Phrase
      • One after another without a break.
      • Arranged in a straight line.
      • Idiom
      • To have an argument.
      A1
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    • in a state

      US

      UK

      • Phrase
      • In a particular condition or situation.
      • In an emotional condition, often negative (e.g., panic, distress).
      B2
      More
    • in a while

      US /ɪn e hwaɪl/

      UK /in ə hwail/

      • Phrase
      • In a short period of time; soon.
      • For a short period of time; soon.
      A2
      More
    • in fact

      US /ɪn fækt/

      UK /in fækt/

      • Adverb
      • Used to emphasize the truth of a statement, especially one that contrasts with or contradicts something else.
      • Used to introduce a more detailed or surprising piece of information.
      • Phrase
      • Used to emphasize the truth of a statement, especially one that is surprising or contrary to what might be expected.
      C1
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    • in mind

      US /ɪn maɪnd/

      UK /in maind/

      • Phrase
      • Being aware of or considering something.
      • To remember or consider something.
      A2
      More
    • in on

      US

      UK

      • Phrase
      • To be involved in a secret or plan.
      • To be aware of something that is secret or not generally known.
      A1
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    • in order to

      US /ɪn ˈɔrdɚ tu/

      UK /in ˈɔ:də tu:/

      • Preposition
      • For the purpose of; with the aim of.
      • Phrase
      • In a specific sequence or arrangement.
      • With the aim of; for the purpose of.
      C1
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    • in other words

      US

      UK

      • Phrase
      • Stating something in a different way, often to make it clearer or more understandable.
      More
    • in the first place

      US

      UK

      • Phrase
      • To begin with; as the first point or consideration.
      • From the beginning; initially.
      A1
      More
    • in writing

      US

      UK

      • Phrase
      • Expressed or presented in written form, rather than spoken.
      • Officially recorded in a written document, especially for legal purposes.
      A1
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    • know about

      US /noʊ əˈbaʊt/

      UK /nəʊ əˈbaut/

      • Phrasal Verb
      • To have information or understanding of a subject or situation.
      More
    • look at

      US /lʊk æt/

      UK /luk æt/

      • Phrasal Verb
      • To use your eyes to focus on something
      • To focus your eyes on something carefully
      A1
      More
    • look for

      US /lʊk fɔr/

      UK /luk fɔ:/

      • Phrasal Verb
      • To try to find a thing or person that is lost
      • To expect or anticipate something.
      A1
      More
    • make some noise

      US

      UK

      • Intransitive Verb
      • To create a loud sound, often to show excitement or approval.
      A1
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    • mess over

      US /mɛs ˈoʊvɚ/

      UK /mes ˈəuvə/

      • other
      • To treat someone unfairly or badly.
      C1
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    • move into

      US /muv ˈɪntu/

      UK /mu:v ˈɪntuː/

      • Phrasal Verb
      • To start living in a new house or building
      • To start being involved in a new area of business or activity.
      More
    • move on

      US /muv ɑn/

      UK /mu:v ɔn/

      • Phrasal Verb
      • To decide to change or go to a different place
      • To start talking about something different.
      A1
      More
    • move to

      US /muv tu/

      UK /mu:v tu:/

      • Phrasal Verb
      • To change the place where you live or work.
      • Verb (Transitive/Intransitive)
      • To proceed to the next stage or action.
      A2
      More
    • much about

      US /mʌtʃ əˈbaʊt/

      UK /mʌtʃ əˈbaut/

      • Phrase
      • A lot of information or knowledge concerning something.
      • To a great extent or degree regarding something; caring.
      A1
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    • next to

      US /nɛkst tu/

      UK /nekst tu:/

      • Preposition
      • Being located along side another
      • In comparison with
      • Adverb
      • Almost; nearly
      A1
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    • odd

      US /ɑd/

      UK /ɒd/

      • Adjective
      • Being unmatched with someone or something
      • Being a number not able to be divided by two
      A2
      More
    • of choice

      US /əv tʃɔɪs/

      UK /əv tʃɔɪs/

      • other
      • Indicating something is preferred or selected deliberately.
      B2
      More
    • of course

      US /ʌv kɔː(r)s/

      UK /ɔv kɔː(r)s/

      • Adverb
      • Sure ; Certainly
      • Phrase
      • For sure; certainly
      A2
      More
    • on a regular basis

      US //ɑn ə ˈrɛgjələr ˈbeɪsəs//

      UK

      • Phrase
      • Happening frequently or at regular intervals.
      B1
      More
    • once in a while

      US //wʌns ɪn ə waɪl//

      UK

      • Phrase
      • Occasionally; not very often.
      • Occasionally; not very often.
      A2
      More
    • one and the same

      US /wʌn ən ðə seɪm/

      UK /wʌn ən ðə seɪm/

      • other
      • Exactly the same person or thing.
      B1
      More
    • one of each

      US

      UK

      • Determiner
      • A single item from every available type or variety.
      • Pronoun
      • A selection including a single item from every option.
      A1
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    • one up

      US /wʌn ʌp/

      UK /wʌn ʌp/

      • Adjective
      • In a better or more advantageous position.
      • Countable Noun
      • An extra life or chance in a video game.
      A1
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    • order in

      US

      UK

      • Phrasal Verb
      • To request food from a restaurant to be delivered to one's home or other location.
      More
    • out of order

      US /aʊt ʌv ˈɔrdɚ/

      UK /aut ɔv ˈɔ:də/

      • Adjective
      • Not in proper working condition; broken.
      • Not following the rules of procedure; inappropriate.
      A1
      More
    • out there

      US /aʊt ðɛr/

      UK /aut ðɛə/

      • Adverb
      • In or to a place that is far away
      • Existing in the universe
      • Adjective
      • Unconventional; strange; avant-garde
      • Existing or available.
      A1
      More
    • pass out

      US /pæs aʊt/

      UK /pɑ:s aut/

      • Phrasal Verb
      • To distribute or hand out papers to people
      • To faint; lose consciousness
      A1
      More
    • pin down

      US /pɪn daʊn/

      UK /pin daun/

      • Phrasal Verb
      • To force someone to clarify their opinion
      • To discover the exact details about something
      • Transitive Verb
      • To force someone to make a decision or give a clear answer.
      A2
      More
    • play around

      US

      UK

      • Phrasal Verb
      • To cheat on your partner romantically
      A1
      More
    • proof

      US /pruf/

      UK /pru:f/

      • Noun (Countable/Uncountable)
      • Act of showing that something exists or is true
      • Special coating that protects something
      • Transitive Verb
      • To read a written work to check for mistakes
      • To protect by painting on a special coating
      A2TOEIC
      More
    • prove

      US /pruv/

      UK /pru:v/

      • Transitive Verb
      • To demonstrate truth by providing evidence
      • To test the quality or worth of something.
      • Intransitive Verb
      • To turn out to be; be found to be.
      A2TOEIC
      More
    • put together

      US /pʊt təˈɡɛðɚ/

      UK /put təˈɡeðə/

      • Phrasal Verb
      • To build or assemble something small, e.g. a toy
      • To organize or arrange something.
      A1
      More
    • row

      US /roʊ/

      UK /rəʊ/

      • Verb (Transitive/Intransitive)
      • To move a boat using oars
      • To argue or quarrel loudly about something
      • Noun (Countable/Uncountable)
      • Loud argument or quarrel between people
      • Straight line of things, e.g. seats in classroom
      A2
      More
    • run by

      US

      UK

      • Phrasal Verb
      • To be managed or controlled by someone or a group.
      • To show or tell something to someone briefly to get their opinion or approval.
      A1
      More
    • score

      US /skɔr, skor/

      UK /skɔ:(r)/

      • Noun
      • A sharp mark or cut in the surface of something
      • Current number of points given in a game, contest
      • Transitive Verb
      • To mark or cut something with a sharp object
      • To get or give points in a game, contest, or test
      A2TOEIC
      More
    • set up

      US /sɛt ʌp/

      UK /set ʌp/

      • Phrasal Verb
      • To make arrangements for something; establish
      • Verb (Transitive/Intransitive)
      • To arrange or prepare something for use.
      • To start a business, organization, etc.
      A1
      More
    • split up

      US /splɪt ʌp/

      UK /split ʌp/

      • Phrasal Verb
      • To break up your marriage or relationship
      • To divide something into smaller parts.
      • Noun
      • A termination of a romantic relationship
      A2
      More
    • start on

      US /stɑrt ɑn/

      UK /stɑ:t ɔn/

      • Phrasal Verb
      • To begin or start doing something.
      • To criticize or complain to someone repeatedly.
      A1
      More
    • start over

      US /stɑrt ˈovɚ/

      UK /stɑ:t ˈəuvə/

      • Phrasal Verb
      • To begin again.
      A1
      More
    • take off

      US /tek ɔf/

      UK /teik ɔf/

      • Phrasal Verb
      • To remove, e.g. your clothes
      • To make arrangements to be absent from work
      • Verb (Transitive/Intransitive)
      • To remove (an item of clothing).
      • To depart; to leave.
      A1
      More
    • talking about

      US

      UK

      • Phrasal Verb
      • To discuss a particular topic.
      • To be constantly mentioning or bringing up a subject.
      A1
      More
    • the following

      US

      UK

      • Adjective
      • Next in order or sequence.
      • Uncountable Noun
      • What is about to be said or written.
      B1
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    • think about

      US /θɪŋk əˈbaʊt/

      UK /θiŋk əˈbaut/

      • Phrasal Verb
      • To consider something carefully.
      • To remember or call to mind.
      A1
      More
    • think of

      US /θɪŋk ʌv/

      UK /θiŋk ɔv/

      • Phrasal Verb
      • To look on as (being something specific); consider
      • To consider or remember something.
      • Verb (Transitive/Intransitive)
      • To imagine or call something to mind
      A1
      More
    • to do with

      US

      UK

      • Phrasal Verb
      • To be about something; concern
      A1
      More
    • to let

      US /tu lɛt/

      UK /tu let/

      • Preposition
      • Indicates that a property is available for rent.
      A2
      More
    • to the left

      US

      UK

      • Phrase
      • In or toward the left direction.
      • Situated on the left side of.
      More
    • to the point

      US /tu ði pɔɪnt/

      UK /tu: ðə pɔint/

      • Adjective
      • Expressing something directly and without unnecessary detail.
      • Phrase
      • Relevant and pertinent to the matter at hand.
      A2
      More
    • turned out

      US

      UK

      • Phrasal Verb
      • To arrive for a public event or entertainment
      • To happen to be in the end
      • Transitive Verb
      • To extinguish or switch off lights.
      A1
      More
    • up against

      US /ʌp əˈɡenst/

      UK /ʌp əˈɡenst/

      • Phrase
      • Facing or contending with something difficult or challenging.
      • In close proximity or contact with something.
      More
    • up there

      US /ʌp ðɛr/

      UK /ʌp ðɛə/

      • Adverb
      • In or to a higher place or position; far away.
      • In heaven.
      A1
      More
    • used to

      US /juzd tu/

      UK /ˈju:st tə/

      • Adjective
      • Did regularly before, but don't do now
      • Auxiliary Verb
      • Have done before, but do not do now
      A1
      More
    • with it

      US /wɪð ɪt/

      UK /wið it/

      • Adjective
      • Intelligent, alert, and up-to-date.
      • Understanding and knowledgeable about current trends or information.
      A1
      More
    • with respect to

      US /wɪð rɪˈspɛkt tu/

      UK /wið risˈpekt tu:/

      • Preposition
      • In relation to; regarding.
      • Phrase
      • In relation to; concerning.
      A1
      More
    • write down

      US /raɪt daʊn/

      UK /rait daun/

      • Phrasal Verb
      • To record in writing
      A1
      More
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    01:03

    She took a brave step forward, leaving behind her comfort zone to chase her dreams.

    Vocabulary
    • brave

      adj. Having courage

    • comfort zone

      phr. A familiar situation where one feels safe

    Explanation
    a brave step is a noun phrase, where brave is an adjective modifying the noun step, meaning "a courageous step". forward is an adverb modifying step, meaning "ahead". The whole phrase serves as the object, answering the "what" of took (verb) — she took a brave step forward.

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    brave

    US/brev/
    UK/breɪv/
    adj.Brave
    v.t.To bravely face
    A2 Elementary

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    A2US
    #proof#induction#professor#move#parity#inaudible

    Lec 3 | MIT 6.042J Mathematics for Computer Science, Fall 2010

    0
    Dou Lin posted on 2016/07/16
    Ever wondered how software bugs happen or how to prove things rigorously? This MIT lecture dives deep into proof techniques like strong induction and invariants, using fun examples like the 8-puzzle! You'll pick up some seriously advanced vocabulary and learn how to spot common proof pitfalls, making it a fantastic watch for anyone interested in computer science and clear thinking.

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