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Does math have a major flaw? - Jacqueline Doan and Alex Kazachek

Video vocabulary

choice

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US / tʃɔɪs /

UK / tʃɔɪs /

A1
  • adjecitve
  • Of good quality or taste; desirable
  • noun
  • Decision between two or more possibilities

mathematical

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US / ˌmæθə'mætɪkl /

UK / ˌmæθəˈmætɪkəl /

A2
  • adjecitve
  • Concerning numbers and equations

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

his

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US / hɪz /

UK / hɪz /

A1
  • pronoun
  • Something belonging to a male person

instance

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US / 'ɪnstəns /

UK / ˈɪnstəns /

A2
  • noun
  • An example of something; case
  • verb
  • To give as an example of something else

percent

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US / pə'sent /

UK / pɚˈsɛnt /

A2
  • adverb
  • One one-hundredth of a whole; the symbol %

upon

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US / əˈpɔn, əpən /

UK / əˈpɑn, əˈpɔn /

A1
  • preposition
  • More formal term for 'on'

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

impractical

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US / ɪmˈpræktɪkl /

UK / ɪmˈpræktɪkəl /

C1
  • adjecitve
  • Not useful or realistically possible

deduction

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US / dɪˈdʌkʃn /

UK / dɪˈdʌkʃən /

B2
  • noun
  • Reaching of a conclusion by using reasoning
  • Fact of being or amount taken away from a total

fundamental

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US / ˌfʌndəˈmentl /

UK / ˌfʌndəˈmɛntl /

A2
  • adjecitve
  • Forming a necessary part, base, or core
  • noun
  • A basic part of something
  • (Music) the lowest note in a harmony

model

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US / ˈmɒdl /

UK / ˈmɑ:dl /

A2
  • adjecitve
  • Being an excellent example of
  • noun
  • Person who wears fashion to show it to the public
  • A small scale copy of a full original
  • verb
  • To wear and display clothes at a fashion show
  • To make a small scale copy of a full original

recombine

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US / ˌri:kəm'baɪn /

UK / ˌrikəmˈbaɪn /

B1
  • verb
  • To put things together to make a whole again

world

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US / wɜ:ld /

UK / wɜrld /

A1
  • noun
  • All the humans, events, activities on the earth
  • Political division due to some kind of similarity

exist

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US / ɪɡ'zɪst /

UK / ɪɡˈzɪst /

A1
  • verb
  • To be present, alive or real

explore

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US / ɪk'splɔ:(r) /

UK / ɪkˈsplɔr /

A2
  • verb
  • To examine something in detail to learn about it
  • To travel to a place to discover more about it

complete

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US / kəm'pli:t /

UK / kəmˈplit /

A1
  • adjecitve
  • Being finished; done; achieved
  • Being as perfect and as total as could be
  • verb
  • To finish or reach the end of doing something

impossibly

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US / ɪm'pɒsəblɪ /

UK / ɪm'pɒsəblɪ /

B1
  • adverb
  • So as not to be possible or acceptable

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

moment

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US / 'məʊmənt /

UK / 'moʊmənt /

A1
  • noun
  • Very short or brief period of time
  • A particular period in time

often

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US / ˈɔfən /

UK / ˈɔfən,ˈɑfən,ˈɔftən,ˈɑf- /

A1
  • adverb
  • Many times; frequently; on many occasions

precise

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US / prɪ'saɪs /

UK / prɪˈsaɪs /

A2
  • adjecitve
  • (Of language details etc.) Very accurate and exact
  • (Of a time, place, quality) exact
  • Being very careful about how you do things

slightly

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US / ˈslaɪtli /

UK / ˈslaɪtli /

B1
  • adverb
  • Only a little

bear

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US / bɛː /

UK / bɛr /

A2
  • noun
  • Large brown animal with fur that lives in forests
  • Someone who expects stock market to fall
  • verb
  • To accept (responsibilities or duties)
  • To give birth to a child; to produce fruit
  • To accept or suffer the weight of difficulties
  • To keep moving left or right while going forward
  • To show (sign of something)
  • To support the weight of something, e.g. a bridge

everyday

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US / ˈevrideɪ /

UK / ˈɛvriˈde /

A1
  • adjecitve
  • Used or seen daily; for daily use; ordinary

freedom

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US / 'fri:dəm /

UK / ˈfridəm /

B1
  • noun
  • State of being free, not being controlled

hand

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US / hænd /

UK / hænd /

A1
  • noun
  • Cards given to a player in a card game
  • Piece of a clock that points to the time
  • Someone who performs physical tasks or work
  • Body part at the end of a person's arm
  • Help for someone performing a particular action
  • Condition of having power or influence
  • Member of the crew of a ship
  • verb
  • To give something to someone personally

summon

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US / 'sʌmən /

UK / ˈsʌmən /

B1
  • verb
  • To order someone to come, e.g. to a court of law

construction

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US / kən'strʌkʃn /

UK / kənˈstrʌkʃən /

A2
  • noun
  • Act of building something; thing that is built
  • Something that is made using different parts
  • The way words are organized in a sentence
  • The way something is made or structured

identical

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US / aɪˈdentɪkl /

UK / aɪˈdɛntɪkəl /

B1
  • adjecitve
  • The same in every way

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

parallel

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US / 'pærəlel /

UK / ˈpærəˌlɛl /

B1
  • adjecitve
  • (Of two lines) at equal distance from each other
  • (Of computer operation) happening at the same time
  • Very similar and often occurring at the same time
  • noun
  • A line on a map a set distance from the equator
  • verb
  • To be equal to, or like, something else
  • To compare

part

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US / pɑ:t /

UK / pɑ:rt /

A1
  • adjecitve
  • To some degree; half; not fully
  • noun
  • Division of a book
  • Ratio of something, e.g. 3 of gin, 1 of tonic
  • A line in a person's hair, made with a comb
  • Character an actor plays on stage, movie, or TV
  • Some, but not all of a specific thing
  • Role in causing something to happen
  • verb
  • To make a line in a person's hair, by using a comb
  • To move two things apart creating a space
  • To leave someone, or to break off a relationship

without

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US / wɪˈðaʊt /

UK / wɪðˈaʊt, wɪθ- /

A1
  • preposition
  • Not with; not having

call

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US / kɔ:l /

UK / kɔl /

A1
  • noun
  • A order or request for action
  • The sound an animal makes, often when in danger
  • A correct prediction, e.g. a decision in a game
  • A short visit to a place or person
  • A decision by a referee or umpire in a game
  • verb
  • To make a request or order for action
  • (Animal) to make sounds to warn of danger
  • To announce the date of an election
  • To make a judgment about something
  • To give someone or something a name
  • To guess in advance the result or outcome
  • To visit a place or person for a short time
  • To phone someone
  • To speak, announce or shout in a loud voice

mathematician

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US / ˌmæθəməˈtɪʃn /

UK / ˌmæθəməˈtɪʃən /

A2
  • noun
  • Student of or teacher of mathematics

proof

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US / pru:f /

UK / pruf /

A2
  • noun
  • Act of showing that something exists or is true
  • Version of a document to be checked for errors
  • Special coating that protects something
  • Something which shows that something else is true
  • verb
  • To read a written work to check for mistakes
  • To protect by painting on a special coating

where

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US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

back

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US / bæk /

UK / bæk /

A1
  • adjecitve
  • Farthest from the front e.g. in a classroom
  • adverb
  • Have returned to a place you were before
  • noun
  • The part of a chair that the upper body leans upon
  • Location at the rear of something
  • The reverse of side something
  • Area on the rear of your body
  • verb
  • To bet money on something
  • To go backwards in a car
  • To support and encourage someone or some cause

lot

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US / lɒt /

UK / lɑt /

A1
  • noun
  • What happens to a person in life from chance; fate
  • A group of people seen together
  • Item for sale at an auction
  • Small area of land used for a purpose e.g. parking

venture

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US / 'ventʃə(r) /

UK / ˈvɛntʃɚ /

B1
  • adjecitve
  • (Business activity) taking chances or risks
  • noun
  • (Business) activity involving calculated risks
  • verb
  • To risk something, such as money
  • To face the dangers, take the risk of something
  • To say something; to dare to speak your mind

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

come

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US / kʌm /

UK / kʌm /

A1
  • verb
  • To arrive at a place
  • (Of mail) to be delivered
  • To move toward someone; go with someone
  • To reach a certain point or state

counterintuitive

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US / kaʊntərɪn'tju:ɪtɪv /

UK / ˌkaʊntərɪn'tju:ɪtɪv /

C2
  • adjecitve
  • Contrary to what common sense would suggest

match

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US / mætʃ /

UK / mætʃ /

A2
  • noun
  • Something that is equal to or the same as another
  • Small stick you strike to light a fire candle etc.
  • A sports competition between two people or teams
  • Person or thing that goes well with another
  • verb
  • To equal or be as good as something else
  • To work well or look good with something else

flawless

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US / 'flɔ:ləs /

UK / ˈflɔlɪs /

B1
  • adjecitve
  • With no imperfections or errors

investigate

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US / ɪn'vestɪɡeɪt /

UK / ɪnˈvɛstɪˌɡet /

A2
  • verb
  • To try to find out facts; to carry out research

lie

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US / laɪ /

UK / lai /

A2
  • noun
  • An untrue statement, when you know it is not true
  • verb
  • To be in a horizontal or flat position
  • To say something that you know is not true

slash

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US / slæʃ /

UK / slæʃ /

B2
  • noun
  • Line ( / ) used in writing
  • Long, deep cut, caused by a sharp object
  • verb
  • To cut violently with a sharp object
  • To decrease something by a large amount

typically

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US / ˈtɪpɪkli /

UK / ˈtɪpɪklɪ /

B1
  • adverb
  • In a normal or usual way

only

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US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

knife

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US / naɪf /

UK / naɪf /

A1
  • noun
  • Long piece of metal you use for cutting things
  • verb
  • To attack someone with a sharp long blade
  • To move through something easily and quickly

meet

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US / mi:t /

UK / mit /

A1
  • noun
  • Sporting competition e.g. swimming
  • verb
  • To provide something that is necessary
  • To come together at a certain time or place

anything

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US / ˈeniθɪŋ /

UK / ˈɛniˌθɪŋ /

A1
  • pronoun
  • A thing of any kind

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

form

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US / fɔ:m /

UK / fɔrm /

A1
  • noun
  • Sports team or person's current winning record
  • Document you complete when making an application
  • Visible shape or style; type; kind
  • verb
  • To organize something such as a club or group
  • To develop; to come into a shape or substance
  • To make something into a particular shape

infinite

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US / 'ɪnfɪnət /

UK / ˈɪnfənɪt /

B2
  • adjecitve
  • Being very large in amount
  • Without an end; limitless; endless

mathematic

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US / ˌmæθɪ'mætɪk /

UK / ˌmæθə'mætɪk /

A1
  • other

gently

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US / ˈdʒentli /

UK / ˈdʒentli /

A2
  • adverb
  • In a mild, careful, and soft manner

issue

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US / 'ɪʃu: /

UK / ˈɪʃu /

A2
  • noun
  • Important topic discussed, debated or argued over
  • Single edition of a magazine
  • verb
  • To make something available to be used or sold
  • To deliver a statement, etc. in an official manner

chooser

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US / tʃu:z /

UK / tʃuz /

A1

foundation

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US / faunˈdeiʃən /

UK / faʊnˈdeʃən /

C1
  • noun
  • Base or important starting point
  • Underground base on which building is constructed
  • Institution supported by a private fund
  • First cosmetic used when putting on makeup
  • Action of establishing an organization

question

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US / 'kwestʃən /

UK / ˈkwɛstʃən /

A1
  • noun
  • Issue or problems you are dealing with
  • What you ask about; issue
  • verb
  • To ask for or try to get information
  • To have or express concerns or uncertainty

extremely

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US / ɪkˈstri:mli /

UK / ɪk'strimlɪ /

B1
  • adverb
  • In a way that is much more than usual or expected

standard

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US / 'stændəd /

UK / ˈstændəd /

A2
  • adjecitve
  • Being the accepted normal level of quality
  • (Of a language) being the most accepted in a place
  • noun
  • Official unit of measuring something
  • Principle of behaving in a moral way

statement

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US / ˈsteɪtmənt /

UK / ˈstetmənt /

A2
  • noun
  • Record of activity in a bank account over time
  • Act or process of saying something formally

system

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US / 'sɪstəm /

UK / ˈsɪstəm /

A1
  • adjecitve
  • Working in an organized, logical way
  • noun
  • Set of organized, planned ideas that work together

imply

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US / ɪmˈplaɪ /

UK / ɪmˈplaɪ /

A2
  • verb
  • To suggest something, without saying it directly

incomprehensible

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US / ɪnˌkɒmprɪˈhensəbl /

UK / ɪnˌkɑ:mprɪˈhensəbl /

B1
  • adjecitve
  • Impossible to understand or comprehend

sound

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US / saʊnd /

UK / saʊnd /

A1
  • adjecitve
  • Sensible, dependable and reliable
  • Unbroken or undisturbed, as of sleep
  • Firm or solid in structure
  • Sane; not mentally ill
  • Clearly reasoned; involving sense, good judgment
  • noun
  • Unique quality that characterizes a style of music
  • Waves traveling in air or water that can be heard
  • verb
  • To seem or appear to be, from what was said
  • To say in a clear deliberate manner
  • To make a noise, e.g. to ring a bell

such

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US / sʌtʃ /

UK / sʌtʃ /

A1
  • determiner
  • Being similar to
  • (Thing) as previously stated or referred to
  • adverb
  • (Used to emphasize the quality of an adjective)

field

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US / fi:ld /

UK / fild /

A1
  • noun
  • Area of study, such as physics or biology
  • Piece of land used to grow crops/raise animals
  • Open area of land, especially without buildings
  • Grassed area where you play some sports
  • verb
  • To respond to something or answer a question
  • To catch or stop a ball during a game

math

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US / mæθ /

UK / mæθ /

A2
  • noun
  • Study or science of numbers and shapes

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

load

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US / ləʊd /

UK / lod /

A2
  • noun
  • Large, often heavy, amount of a thing to be moved
  • A burden; heavy responsibility
  • Many or much of something; a lot of
  • Items that fill a truck, machine
  • verb
  • To put in items for use (e.g. bullets in a gun)

line

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US / laɪn /

UK / laɪn /

A1
  • noun
  • Border that divides two places or regions
  • Long crease in the skin, often from age
  • Mark that is long, straight and very thin
  • Row of words, letters or numbers that are written
  • Telephone connection
  • People waiting one behind the other; queue
  • Long thin wire, e.g. for electrical signal
  • verb
  • To put material along the inside of something

modern

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US / ˈmɔdən /

UK / ˈmɑdən /

A1
  • adjecitve
  • Of the present time; up to date; contemporary

tension

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US / 'tenʃn /

UK / ˈtɛnʃən /

A2
  • noun
  • Feeling of anxiety and inability to relax
  • Degree to which something is stretched tight

finite

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US / ˈfaɪnaɪt /

UK / ˈfaɪˌnaɪt /

B1
  • adjecitve
  • Having limits; lasting for a limited time

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

hyperbolic

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US / ˌhaɪpəˈbɒlɪk /

UK / ˌhaɪpɚˈbɑlɪk /

A1
  • adjecitve
  • Enlarged beyond truth or reasonableness

logic

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US / ˈlɒdʒɪk /

UK / ˈlɑ:dʒɪk /

A2
  • noun
  • Proper, valid sensible reasoning
  • Scientific study of reasoning

sharp

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US / ʃɑ:p /

UK / ʃɑrp /

A2
  • adjecitve
  • Being very clear and easy to see
  • (Of clothes) nicely or stylishly
  • Being able to think, see, or understand quickly
  • Having a thin edge or point that is able to cut
  • Requiring a quick or sudden change in direction
  • Having a flavor that is very strong and distinct
  • adverb
  • At precisely the time given
  • Suddenly; immediately (of directions)
  • noun
  • Person's name
  • A musical tone

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

through

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US / θru: /

UK / θru /

A2
  • adjecitve
  • having finished using or doing something
  • adverb
  • From the beginning of something until the end
  • preposition
  • Over, in, across an entire thing or place
  • Allowing you to pass between, or to
  • By a particular way or process; by the use of

set

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US / set /

UK / sɛt /

A1
  • adjecitve
  • Prepared for something; ready
  • noun
  • Complete group of something
  • Place where a television show or movie is filmed
  • Group of games in a tennis match
  • Device that receives radio or television signals
  • verb
  • To make a clock state or ring at a particular time
  • To decide upon or choose something
  • To make something ready for use (e.g. table)
  • To decide on a price for something
  • To become hard (of glue, concrete etc.)
  • To be located in a specific place or time
  • To put (e.g. a vase) down carefully in a place
  • To put someone in a certain condition or state
  • (Of the sun) to go lower than the horizon

start

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US / stɑ:t /

UK / stɑrt /

A1
  • noun
  • First time or place that a thing exists; beginning
  • First opportunity to achieve something, e.g. a job
  • Sudden action or movement because you are scared
  • other
  • Beginning of something in place or time
  • verb
  • To do, be or happen for the first time; begin
  • To turn something on

within

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US / wɪˈðɪn /

UK / wɪðˈɪn, wɪθ- /

A1
  • adverb
  • Inside the limits of an area, time or range
  • preposition
  • From the inside of something

always

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US / 'ɔ:lweɪz /

UK / ˈɔlwez,-wɪz,-wiz /

A1
  • adverb
  • For a very long time
  • At all times; in every situation
  • For ever

many

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US / 'menɪ /

UK / ˈmɛni /

A1
  • determiner
  • Used to refer a large number of things

scenario

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US / sɪˈnɑː.ri.əʊ /

UK / səˈner.i.oʊ /

B1
  • noun
  • An imagined sequence of events in a plan/project

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

alien

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US / 'eɪlɪən /

UK / ˈeliən,ˈeljən /

B1
  • adjecitve
  • Being foreign, different or unfamiliar
  • noun
  • Foreigner; a person not from this place
  • Person or creature from a planet other than Earth

day

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US / deɪ /

UK / de /

A1
  • noun
  • A period of 24 hours beginning at midnight
  • The period of time when it is light outside
  • Person's name

ever

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US / 'evə(r) /

UK / ˈɛvɚ /

A1
  • adverb
  • At any time; at all times in the future

point

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US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

basic

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US / 'beɪsɪk /

UK / ˈbesɪk /

A1
  • adjecitve
  • At the most important or easiest (beginner) level

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

declare

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US / dɪ'kleə(r) /

UK / dɪˈklɛr /

A2
  • verb
  • To make a statement in a strong and confident way
  • To show the cost of things purchased overseas
  • To say something in an official or sure way

contain

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US / kənˈteɪn /

UK / kənˈten /

A2
  • verb
  • To keep something from spreading
  • To hold something inside something else

geometry

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US / dʒiˈɒmətri /

UK / dʒiˈɑ:mətri /

B2
  • noun
  • Mathematical study of shapes, surfaces, and space
  • Mathematical shape of something

matter

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US / 'mætə(r) /

UK / ˈmætɚ /

A1
  • noun
  • Material all things are made of that fills space
  • Problem or reason for concern
  • verb
  • To be of great importance; to count

stem

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US / stem /

UK / stɛm /

B1
  • noun
  • Long thin central part of a plant, bearing leaves
  • Long thin part supporting something e.g. a light
  • Main part of a word, e.g. 'use' in 'useful'
  • verb
  • To remove the stem of a flower or fruit
  • To start from or be the origin of
  • To stop something bad from spreading or developing

while

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US / waɪl /

UK / hwaɪl, waɪl /

A1
  • conjunction
  • In spite of the fact that; although
  • During the time that; at the same time
  • noun
  • Short amount of time

coexist

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US / ˌkəʊɪɡ'zɪst /

UK / ˌkoɪɡˈzɪst /

B2
  • verb
  • To exist peacefully together

beautiful

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US / 'bju:tɪfl /

UK / ˈbjutəfəl /

A1
  • adjecitve
  • Having dome something well
  • Being very attractive or appealing physically

consider

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US / kən'sɪdə(r) /

UK / kənˈsɪdər /

A1
  • verb
  • To think carefully about something

fortunately

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US / ˈfɔ:tʃənətli /

UK / ˈfɔ:rtʃənətli /

A2
  • adverb
  • Through good luck; luckily

reality

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US / rɪ'ælətɪ /

UK / riˈælɪti /

A2
  • noun
  • What is true, as opposed to what is imagined

visit

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US / ˈvɪzɪt /

UK / ˈvɪzɪt /

A1
  • noun
  • Trip to a place for a time, usually for a reason
  • verb
  • To go to a place for a time, usually for a reason

true

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US / tru: /

UK / tru: /

A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

continue

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US / kən'tɪnju: /

UK / kənˈtɪnju /

A1
  • verb
  • To do something without stopping, or after pausing
  • To start doing again after a break, pause, or stop

should

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US / ʃʊd /

UK / ʃʊd /

A1
  • other
  • Used to indicate what is proper or reasonable

truth

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US / tru:θ /

UK / truθ /

A2
  • noun
  • Real facts about something

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

intuition

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US / ˌɪntjuˈɪʃn /

UK / ˌɪntuˈɪʃən, -tju- /

B2
  • noun
  • Natural ability to guess or feel things

logically

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US / 'lɒdʒɪklɪ /

UK / ˈlɑdʒɪkl:ɪ /

A2
  • adverb
  • In a reasonable and practical manner

marble

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US / 'mɑ:bl /

UK / ˈmɑrbəl /

B1
  • noun
  • A hard type of stone, often used in monuments

new

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US / nju: /

UK / nu, nju /

A1
  • adjecitve
  • Not old, recently born, built or made
  • Being or doing something for the first time
  • Not felt, seen or known previously
  • Having been recently bought or obtained

try

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US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

interesting

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US / ˈɪntrəstɪŋ /

UK / ˈɪntrɪstɪŋ, -tərɪstɪŋ, -təˌrɛstɪŋ /

A1
  • adjecitve
  • Taking your attention; making you want to know
  • verb
  • To make someone want to know about something
  • To persuade to do, become involved with something

nothing

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US / 'nʌθɪŋ /

UK / ˈnʌθɪŋ /

A1
  • noun
  • Item of little or no value, importance, interest
  • Number or value of zero
  • pronoun
  • Not anything, not a single thing

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

ball

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US / bɔ:l /

UK / bɔl /

A1
  • noun
  • Large dance where people dress formally
  • Small round object often used in a game or sport

own

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US / əʊn /

UK / on /

A1
  • adjecitve
  • Belong to oneself
  • determiner
  • Yours, his, hers, etc.; not belonging to another
  • pronoun
  • (Something) belong to myself
  • verb
  • To have something as your property

straightforward

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US / ˌstreɪtˈfɔ:wəd /

UK / stretˈfɔrwəd /

B1
  • adjecitve
  • Easy to do or understand; not complicated

analysis

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US / əˈnæləsɪs /

UK / əˈnælɪsɪs /

B1
  • noun
  • Careful study to better understand something

element

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US / 'elɪmənt /

UK / ˈɛləmənt /

A2
  • noun
  • Essential or particular part of something

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

spherical

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US / ˈsferɪkl /

UK / ˈsfɪrɪkəl, ˈsfɛr- /

B1
  • adjecitve
  • Round and shaped like a ball

conclusion

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US / kənˈklu:ʒn /

UK / kənˈkluʒən /

A2
  • noun
  • End of something; finish
  • Judgment or opinion after thinking for a while
  • Opinion or final judgment at end of book, essay

frantically

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US / 'fræntɪklɪ /

UK / ˈfræntɪklɪ /

B2
  • adverb
  • In a frenzied, wildly excited or worried way

grossly

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US / ˈgrəʊsli /

UK / ˈgroʊsli /

B1
  • adverb
  • In a disgusting manner or with bad taste

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

require

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US / rɪ'kwaɪə(r) /

UK / rɪˈkwaɪr /

A2
  • verb
  • To demand that someone does something
  • To need to do something, to make it necessary

bizarre

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US / bɪˈzɑ:(r) /

UK / bɪˈzɑr /

B2
  • adjecitve
  • Odd or strange

example

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US / ɪgˈzɑ:mpl /

UK / ɪɡˈzæmpəl /

A1
  • noun
  • Thing, person which represents a category

each

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US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

recommend

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US / ˌrekə'mend /

UK / ˌrɛkəˈmɛnd /

A2
  • verb
  • To advise or suggest that someone do something

house

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US / haʊs /

UK / haʊs /

A1
  • noun
  • Place where a specific activity or business occurs
  • Building in which a family, person lives
  • verb
  • To give someone a place to live
  • To contain or store something

select

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US / sɪ'lekt /

UK / sɪˈlɛkt /

A2
  • verb
  • To choose a suitable thing from a group

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

she

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US / ʃɪ /

UK / ʃi /

A1
  • pronoun
  • Female person or animal mentioned before
  • (Refers to female person mentioned before)

thirty

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US / 'θɜ:tɪ /

UK / ˈθə:ti /

A1
  • number
  • 30

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

again

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US / ə'ɡen /

UK / əˈɡɛn /

A1
  • adverb
  • One more time, once more

even

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US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

down

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US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

step

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US / step /

UK / stɛp /

A1
  • noun
  • Movement done as part of a particular dance
  • Distance covered by one movement of a leg; stride
  • One part or stage in a process
  • Sound made by the feet while walking; footstep
  • Flat horizontal piece that forms stairs
  • verb
  • To raise and moving the foot to put it down

possible

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US / ˈpɒsəbl /

UK / ˈpɑsəbəl /

A1
  • adjecitve
  • Being able or appropriate for a task or purpose
  • Having a chance of happening, or being true

else

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US / els /

UK / ɛls /

A1
  • adverb
  • Otherwise; if you fail to
  • (Of person place thing etc.) besides; in addition

move

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US / mu:v /

UK / muv /

A1
  • noun
  • Act of moving a playing piece in chess, etc.
  • An action; doing something
  • Step taken to achieve a goal
  • verb
  • To cause someone to have certain emotions
  • To cause something to change to a different place
  • To change where people live or a business operates
  • To take action to do or achieve something

section

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US / 'sekʃn /

UK / ˈsɛkʃən /

B1
  • noun
  • A part of a whole
  • Specific area or region within a larger place
  • Specific group of people from a larger group
  • Part of a book, newspaper, etc.
  • verb
  • To divide something into smaller parts

their

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US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

useful

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US / ˈju:sfl /

UK / ˈjusfəl /

A1
  • adjecitve
  • That can help with a particular task

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

common

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US / 'kɒmən /

UK / ˈkɑmən /

A1
  • adjecitve
  • Shared; Belonging to or used by everyone
  • Typical, normal; not unusual
  • noun
  • Area in a city or town that is open to everyone
  • Field near a village owned by the local community

its

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US / ɪts /

UK / ɪts /

A1
  • adjecitve
  • Referring to or belonging to ‘it’
  • determiner
  • Of something; belonging or related to something
  • other
  • Possessive form of “it”

produce

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US / prə'dju:s /

UK / prəˈdus, -ˈdjus, pro- /

A1
  • noun
  • Fresh foods such as fruits and vegetables
  • verb
  • To grow something naturally
  • To make something appear
  • To manufacture something using machines
  • To control the making a movie or television show

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

omniscient

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US / ɒmˈnɪsiənt /

UK / ɑ:mˈnɪsiənt /

C1
  • adjecitve
  • All-knowing

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

euclidean

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US / ju:ˈklidiən /

UK / juˈklɪdiən /

A1
  • other
  • Relating to geometry as developed by Euclid

crucial

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US / 'kru:ʃl /

UK / ˈkruʃəl /

B1
  • adjecitve
  • Extremely important or necessary

approach

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US / ə'prəʊtʃ /

UK / əˈprəʊtʃ /

A2
  • noun
  • Means of reaching a place, often a road or path
  • Request of someone with a specific goal in mind
  • Specific way to handle a project, task, problem
  • verb
  • To get close to reaching something or somewhere
  • To request someone to do something specific

functional

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US / ˈfʌŋkʃənl /

UK / ˈfʌŋkʃənəl /

A2
  • adjecitve
  • Useful; not just for decoration

result

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US / rɪ'zʌlt /

UK / rɪˈzʌlt /

A2
  • noun
  • Something produced through tests or experiments
  • Final score of a competition, election or game
  • verb
  • To be the outcome of other causes and effects

theory

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US / ˈθiəri /

UK / ˈθiəri, ˈθɪri /

A2
  • noun
  • Ideas or principles that explain facts or events

abstract

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US / 'æbstrækt /

UK / ˈæbˌstrækt /

B1
  • adjecitve
  • Concerning something that doesn't exist physically
  • noun
  • Passage of text from an article or book
  • Something that doesn't exist physically
  • Short summary of an academic article
  • verb
  • To take out or remove a part of
  • To summarize an academic article

between

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US / bɪˈtwi:n /

UK / bɪˈtwin /

A1
  • preposition
  • From one person, thing, or place, to another
  • In the space that separates two objects
  • Among two or more people who share something

everything

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US / 'evrɪθɪŋ /

UK / ˈɛvriˌθɪŋ /

A1
  • pronoun
  • All of the things mentioned

indistinguishable

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US / ˌɪndɪˈstɪŋgwɪʃəbl /

UK / ˌɪndɪˈstɪŋɡwɪʃəbəl /

B1
  • adjecitve
  • Exactly alike; not able to be seen as different

original

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US / ə'rɪdʒənl /

UK / əˈrɪdʒənəl /

A2
  • adjecitve
  • Being first made, thought or performed; fresh
  • Being unique or thinking differently from others

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

build

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US / bɪld /

UK / bɪld /

A1
  • noun
  • Your physical shape; physique
  • verb
  • To establish e.g. a reputation, over time
  • To construct a house, office, factory

distinguishable

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US / dɪ'stɪŋɡwɪʃəbl /

UK / dɪˈstɪŋɡwɪʃəbl: /

A2
  • adjecitve
  • Able to be perceived as different or distinct

fill

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US / fɪl /

UK / fɪl /

A1
  • noun
  • Act of filling; amount used to make something full
  • verb
  • To make something full
  • To move into all parts of an area
  • To repair a surface by adding a substance to it
  • To use (time); to do something during

work

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US / wɜ:k /

UK / wɚk /

A1
  • adjecitve
  • Activity completed in order to make money
  • noun
  • The product of some artistic or literary endeavor
  • Everything created by an author, artist, musician
  • Activity you do in order to make money
  • Place of employment
  • Final product or result of a some labor or effort
  • verb
  • To bring into a specific state of success
  • To be functioning properly, e.g. a car
  • To do your job in your company or workplace
  • To make an effort to do something
  • To operate a machine or device

physical

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US / ˈfɪzɪkl /

UK / ˈfɪzɪkəl /

A2
  • adjecitve
  • Concerning the body of a person
  • Concerning things that can be seen or touched
  • noun
  • Health check at the doctors' or hospital

construct

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US / kənˈstrʌkt /

UK / kənˈstrʌkt /

A2
  • noun
  • A thought, theory or hypothesis
  • verb
  • To build or create something
  • To create a sentence, story, argument or theory

also

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US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

five

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US / faɪv /

UK / faɪv /

A1
  • number
  • 5

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

live

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US / lɪv /

UK / liv /

A1
  • adjecitve
  • Being broadcast as events happen, not recorded
  • Carrying electric current; able to give a shock
  • Glowing because burning; hot
  • Not yet killed (for food)
  • adverb
  • (Music, drama) as it is performed
  • verb
  • To be alive
  • To experience a particular type of life
  • To make your home in a house or town

year

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US / jə: /

UK / jɪr /

A1
  • noun
  • Unit of time equal to 12 months or 365 or 366 days
  • Used to refer to the age of a person

absurd

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US / əb'sɜ:d /

UK / əbˈsɚd, -ˈzɚd /

B1
  • adjecitve
  • So foolish as to be difficult to believe

intuit

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US / ɪnˈtju:ɪt /

UK / ɪnˈtu:ɪt /

A1
  • other
  • Know or grasp by intuition or feeling

lead

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US / li:d /

UK / lid /

A1
  • adjecitve
  • Being the main part in movies or plays
  • noun
  • Wire for electricity, computer, etc.; cable
  • Information that could help to solve a crime
  • Main part in a play or movie
  • Heavy, gray metal element
  • Rope used to tie something to stop it escaping
  • Act of being at the front in a race or game
  • verb
  • To show the way or guide others
  • To be at the front of a race or game
  • To travel in front of; go in advance of others

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

might

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US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

advance

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US / əd'vɑ:ns /

UK / ædˈvæns /

A2
  • noun
  • Forward movement by an army
  • An attempt to seduce someone
  • verb
  • (Of an army) to move forward
  • To change or improve
  • To increase in price or value
  • To move forward in a certain direction
  • To try to seduce someone

axiom

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US / ˈæksiəm /

UK / ˈæksiəm /

C1
  • noun
  • A generally accepted rule or statement generally

equally

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US / ˈi:kwəli /

UK / ˈiːkwəli /

A1
  • adverb
  • In an equal, even, or identical manner

fate

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US / feɪt /

UK / fet /

B1
  • noun
  • What will happen to you in the future, often bad
  • Power that determines what happens; destiny

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

universe

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US / ˈju:nɪvɜ:s /

UK / ˈjunəˌvɚs /

B2
  • noun
  • All of space that contains planets and stars
  • Things surrounding a person, affecting their life

into

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US / 'ɪntə /

UK / ˈɪntu /

A1
  • preposition
  • Moving or going inside something
  • In the same direction as; in the direction of
  • So as to become; taking the state of

perfect

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US / 'pɜ:fɪkt /

UK / ˈpɚfɪkt /

A1
  • adjecitve
  • So good it cannot be improved
  • verb
  • To do something so well, it cannot be done better

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

statistic

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US / stəˈtɪstɪk /

UK / stəˈtɪstɪk /

B1
  • noun
  • Number that represents a piece of information

follow

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US / ˈfɔləu /

UK / ˈfɑlo /

A1
  • verb
  • To come after someone; be guided by someone
  • To support someone, e.g. singer or comedian
  • To be the logical result of something
  • To happen after something else happens
  • To believe a set of values or a moral teacher
  • To understand something happening or being said

goal

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US / ɡəʊl /

UK / ɡol /

A2
  • noun
  • Something you try to do or achieve; an aim
  • (Sports) net into which you put a ball to score
  • (Sports) act of scoring by putting a ball in a net

free

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US / fri: /

UK / fri /

A1
  • adjecitve
  • Living, happening without being controlled
  • Costing no money
  • Not working; not busy
  • verb
  • To release (e.g. bird) from a cage or prison

happy

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US / ˈhæpi /

UK / ˈhæpi /

A1
  • adjecitve
  • Feeling pleasure or joy; glad

play

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US / pleɪ /

UK / pleɪ /

A1
  • noun
  • Loose, free movement between two objects
  • Single action in a sports game
  • Performance in which people act in a theater
  • verb
  • To act as a character in a movie, or on stage
  • To perform music on an instrument
  • To use a device, e.g. a video game
  • To do something for enjoyment and fun
  • To do or perform a game or sport

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

valid

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US / 'vælɪd /

UK / ˈvælɪd /

A2
  • adjecitve
  • Being in effect or in force, often legally
  • Reasonable; based on sound assumptions
  • Working correctly; producing results

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

alongside

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US / əˌlɒŋˈsaɪd /

UK / əˌlɔ:ŋˈsaɪd /

B1
  • preposition
  • Side by side with something

experience

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US / ɪk'spɪərɪəns /

UK / ɪkˈspɪriəns /

A1
  • noun
  • Thing a person has done or that happened to them
  • An event at which you learned something
  • Knowledge gained by living life, doing new things
  • verb
  • To gain knowledge by doing things

law

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US / lɔ: /

UK / lɔ /

A1
  • noun
  • Field of study that relates to the legal profession
  • A rule made and enforced by a government
  • System or rules made by the government

measure

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US / ˈmeʒə(r) /

UK / ˈmɛʒɚ /

A1
  • noun
  • Plan to achieve a desired result
  • Tool used to calculate the size of something
  • verb
  • To determine the value or importance of something
  • To calculate size, weight or temperature of

structure

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US / ˈstrʌk.tʃə /

UK / ˈstrʌk.tʃɚ /

A2
  • noun
  • The way in which the parts of a system or object are arranged or organized, or a system arranged in
  • verb
  • To plan, organize, or arrange the parts of something

effect

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US / ɪ'fekt /

UK / ɪˈfɛkt /

A1
  • noun
  • An advantage, benefit
  • Change brought about by a cause; result

sense

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US / sens /

UK / sɛns /

A1
  • noun
  • Certain mental feeling or emotion
  • Normal or clear state of mind
  • Meaning of a particular word, phrase or text
  • verb
  • To perceive using sight, sound, taste touch etc.
  • To recognize the presence of something

whether

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US / ˈweðə(r) /

UK / ˈhwɛðɚ, ˈwɛð- /

A1
  • conjunction
  • If something will happen or not

support

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US / səˈpɔ:t /

UK / səˈpɔrt, -ˈport /

A1
  • noun
  • Assistance or advice given to someone
  • Evidence that helps prove something is true
  • A thing to hold up or prevent from falling down
  • verb
  • To give assistance or advice to someone
  • To help prove or show that something is true
  • To hold up or prevent from falling down

box

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US / bɒks /

UK / bɑ:ks /

A1
  • noun
  • A marked area of a baseball field
  • A container with four straight sides and a lid
  • Area of seating in a theater separated from others
  • A 4 sided container or shape printed on a page
  • Entire amount of something inside a container
  • verb
  • To strike someone on the side of the head
  • To pack an object in a six-sided container
  • To fight with gloved hands as a sport

mysterious

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US / mɪˈstɪəriəs /

UK / mɪˈstɪriəs /

A2
  • adjecitve
  • Unusual; hard to understand or work out

stab

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US / stæb /

UK / stæb /

B1
  • verb
  • To strike a blow with a knife, as to kill someone

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

apply

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US / ə'plaɪ /

UK / əˈplaɪ /

A1
  • verb
  • To spread a substance or liquid over a surface
  • To commit your time and effort to doing something
  • To make something useful in a certain situation
  • To be relevant for a situation
  • To ask formally for (job, permission etc.)

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

zero

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US / ˈzɪərəʊ /

UK / ˈzɪroʊ /

A1
  • noun
  • Temperature when water turns to ice
  • number
  • Number 0
  • verb
  • To set a scale or other device to show 0

vastly

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US / ˈvɑ:stli /

UK / ˈvæstli /

B2
  • adverb
  • To an exceedingly great extent or degree

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

copy

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US / ˈkɒpi /

UK / ˈkɑ:pi /

A1
  • noun
  • A counter for items that are the same
  • Fake product pretending to be an original
  • An imitation of an original
  • A duplicate of a paper printed in a photocopier
  • Written text for printing, use in ads, etc.
  • verb
  • To make something look the same as the original
  • To act in the exact same way as someone else
  • To read and then write down what you read

reject

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US / rɪˈdʒekt /

UK / rɪˈdʒɛkt /

A2
  • noun
  • Goods that are not suitable for sale at full price
  • Person others do not like, or refuse to accept
  • verb
  • To decide that something is not good enough
  • To refuse, deny to believe, accept, or consider

physics

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US / ˈfɪzɪks /

UK / ˈfɪzɪks /

A1
  • other
  • The study of heat, light, and energy on objects

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

distribute

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US / dɪˈstrɪbju:t /

UK / dɪˈstrɪbjut /

A2
  • verb
  • To hand out or give to people
  • To send products to stores to sell
  • To spread something over an area

infinitely

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US / ˈɪnfɪnətli /

UK / ˈɪnfənɪtlɪ /

B2
  • adverb
  • Continuing forever without end; very great

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)
  • Subtitles section
  • Consider this mathematician with her standard issue infinitely sharp knife and a perfect ball.
  • She frantically slices and distributes the ball into an infinite number of boxes.
  • She then recombines the parts into five precise sections.
  • Gently moving and rotating these sections around, seemingly impossibly, she recombines them to form two identical, flawless, and complete copies of the original ball.
  • This is a result known in mathematics as the Banach Tarski paradox.
  • The paradox here is not in the logic or the proof, which are like the balls, flawless, but instead in the tension between mathematics and our own experience of reality.
  • And in this tension lives some beautiful and fundamental truths about what mathematics actually is.
  • We'll come back to that in a moment, but first we need to examine the foundation of every mathematical system—axioms.
  • Every mathematical system is built and advanced by using logic to reach new conclusions.
  • But logic can't be applied to nothing.
  • We have to start with some basic statements, called axioms, that we declare to be true, and make deductions from there.
  • Often these match our intuition for how the world works.
  • For instance, that adding zero to a number has no effect is an axiom.
  • If the goal of mathematics is to build a house, axioms form its foundation— the first thing that's laid down that supports everything else.
  • Where things get interesting is that by laying a slightly different foundation, you can get a vastly different but equally sound structure.
  • For example, when Euclid laid his foundations for geometry, one of his axioms implied that given a line and a point off the line,
  • only one parallel line exists going through that point.
  • But later mathematicians, wanting to see if geometry was still possible without this axiom, produced spherical and hyperbolic geometry, each valid, logically sound, and useful in different contexts.
  • One axiom common in modern mathematics is the axiom of choice.
  • It typically comes into play in proofs that require choosing elements from sets.
  • which we'll grossly simplify to marbles in boxes.
  • For our choices to be valid, they need to be consistent— meaning if we approach a box, choose a marble, and then go back in time and choose again, we'd know how to find the same marble.
  • If we have a finite number of boxes, that's easy.
  • It's even straightforward when there are infinite boxes if each contains a marble that's readily distinguishable from the others.
  • It's when there are infinite boxes with indistinguishable marbles that we have trouble.
  • But in these scenarios, the axiom of choice lets us summon a mysterious, omniscient chooser that will always select the same marbles— without us having to know anything about how those choices are made.
  • Our stab happy mathematician, following Banach and Tarski's proof, reaches a step in constructing the five sections where she has infinitely many boxes filled with indistinguishable parts.
  • So she needs the axiom of choice to make their construction possible.
  • If the axiom of choice can lead to such a counterintuitive result, should we just reject it?
  • Mathematicians today say no, because it's load bearing for a lot of important results in mathematics.
  • Fields like measure theory and functional analysis, which are crucial for statistics and physics, are built upon the axiom of choice.
  • While it leads to some impractical results, it also leads to extremely practical ones.
  • Fortunately, just as Euclidean geometry exists alongside hyperbolic geometry, mathematics with the axiom of choice coexists with mathematics without it.
  • The question for many mathematicians isn't whether the axiom of choice, or for that matter any given axiom, is right or not, but whether it's right for what you're trying to do.
  • The fate of the Banach Tarski paradox lies in this choice.
  • This is the freedom mathematics gives us.
  • Not only is it a way to model our physical universe using the axioms we intuit from our daily experiences, but a way to venture into abstract mathematical universes and explore arcane geometries and laws unlike anything we can ever experience.
  • If we ever meet aliens, axioms which seem absurd and incomprehensible to us might be everyday common sense to them.
  • To investigate, we might start by handing them an infinitely sharp knife and a perfect ball and see what they do.
  • If you're looking for a free and easy way to continue your exploration of the beautiful and bizarre within the world of math, we'd recommend Brilliant.org.
  • If you visit Brilliant.org slash TED Ed today, you can get thirty days free and twenty percent off a year of STEM learning.