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Infinity Paradoxes - Numberphile

Video vocabulary

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

chance

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US / tʃɑ:ns /

UK / tʃæns /

A1
  • adjecitve
  • Happening by luck; not planned
  • Taking a risk to try something
  • noun
  • The way something happens without planning
  • An opportunity; favorable circumstances, situation
  • The possibility that something will happen
  • verb
  • To occur just through luck; happen
  • To take a risk to try something

everyone

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US / ˈevriwʌn /

UK / ˈɛvriˌwʌn /

A1
  • pronoun
  • Every person; everybody

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”

strange

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US / streɪndʒ /

UK / strendʒ /

A1
  • adjecitve
  • Unusual or odd; surprising because unexpected

change

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US / tʃeɪndʒ /

UK / tʃendʒ /

A1
  • noun
  • Exchange of one set of clothes for another
  • Money in the form of coins instead of paper
  • Money returned after giving too much
  • Act of making or becoming something else
  • verb
  • To exchange one set of clothes for another
  • To exchange one kind of money for another
  • To replace something with another thing
  • To make or become something else
  • To go from one train, bus, etc. and go to another

philosopher

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US / fəˈlɒsəfə(r) /

UK / fɪˈlɑsəfɚ /

C1
  • noun
  • Person studying the meaning of truth and life

show

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US / ʃəʊ /

UK / ʃo /

A1
  • noun
  • False display of love, emotion or action
  • An event for displaying or promoting goods
  • Play, opera or theater production
  • Presentation that is broadcast on TV or radio
  • verb
  • To be easily seen or displayed
  • To display your emotions or feelings
  • To let someone see something; display
  • To explain or teach how something is done
  • To lead someone somewhere; point them to something
  • To prove something to be true, correct
  • To reveal or allow something to be seen

theory

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US / ˈθiəri /

UK / ˈθiəri, ˈθɪri /

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

believe

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US / bɪ'li:v /

UK / bɪˈliv /

A1
  • verb
  • To think or accept that something is true
  • To have a particular opinion about something

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

customer

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US / ˈkʌstəmə(r) /

UK / ˈkʌstəmɚ /

A2
  • noun
  • Someone who buys goods or services from a business

human

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US / 'hju:mən /

UK / ˈhjumən /

A1
  • adjecitve
  • Concerning or characteristic of people
  • noun
  • A person; a man, woman or child

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

nature

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US / 'neɪtʃə(r) /

UK / ˈnetʃɚ /

A1
  • noun
  • Person's character or particular way of behaving
  • Basic look, feel or function of something
  • Physical world, including plants, animals, rocks

pay

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US / peɪ /

UK / pe /

A1
  • noun
  • Money you receive from your job, work, etc.
  • verb
  • To give money for goods or work done
  • To give (attention, respect, etc.) to
  • To be punished or suffer for something you did
  • To make (a visit) to a person or place

account

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US / ə'kaʊnt /

UK / əˈkaʊnt /

A1
  • noun
  • An advantage
  • Arrangement with a bank to keep your money for you
  • An invoice for things bought
  • Arrangement whereby you can use online services
  • A description, often written, of events; report

casino

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US / kəˈsi:nəʊ /

UK / kəˈsi:noʊ /

B2
  • noun
  • Establishment that hosts legalized gambling

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

room

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US / ru:m /

UK / rum, rʊm /

A1
  • noun
  • All of the people inside a particular room
  • Part of building enclosed by walls, e.g. kitchen
  • Opportunity to exist, happen, or be true
  • verb
  • To share a home with someone

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

bet

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US / bet /

UK / bet /

A2
  • noun
  • Act of gambling money on the result of a race etc.
  • verb
  • To gamble money to win more money, e.g. on horses

desk

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US / desk /

UK / dɛsk /

A1
  • noun
  • Piece of furniture like a table often with drawers

figure

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US / ˈfiɡə /

UK / ˈfɪɡjɚ /

A1
  • noun
  • Your body shape
  • Numbers in a calculation
  • Doll-like thing meant to represent a person
  • Picture or diagram giving information in a text
  • Person who is very important or famous
  • Shape of a person seen indistinctly or in outline
  • Amount that is expressed in numbers
  • verb
  • To appear in a game, play or event
  • To calculate how much something will cost
  • To understand after thinking; work out

else

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US / els /

UK / ɛls /

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

guarantee

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US / ˌɡærən'ti: /

UK / ˌɡærənˈti /

A2
  • noun
  • A promise to repair a broken product
  • Promise that something will be done as expected
  • verb
  • To promise to repair a broken product
  • To promise that something will happen or be done
  • To promise to pay if another person fails to do so

hotel

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US / həʊ'tel /

UK / hoˈtɛl /

A1
  • noun
  • Place where people can stay when traveling

their

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US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

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

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

bucket

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US / 'bʌkɪt /

UK / ˈbʌkɪt /

B1
  • noun
  • Open container with a handle used to carry liquids

everything

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US / 'evrɪθɪŋ /

UK / ˈɛvriˌθɪŋ /

A1
  • pronoun
  • All of the things mentioned

topic

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US / 'tɒpɪk /

UK / ˈtɑpɪk /

A2
  • noun
  • Subject or issue people talk or write about

they

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US / ðeɪ /

UK / ðe /

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

very

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US / 'verɪ /

UK / ˈvɛri /

A1
  • adjecitve
  • Concerning a large degree or amount
  • adverb
  • A lot; much; many
  • Used to stress or emphasize a noun

volume

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US / ˈvɒlju:m /

UK / ˈvɑljum, -jəm /

A2
  • noun
  • Number or amount of something e.g. sales
  • Amount of space that something takes up
  • One book that is part of a set of books
  • Level of sound produced by radio or television

fourth

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US / fɔ:θ /

UK / fɔ:rθ /

A1
  • noun
  • 4th

throw

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US / θrəʊ /

UK / θroʊ /

A1
  • noun
  • Arm movement to make a thing fly through the air
  • Loose cloth or blanket (usually over a chair)
  • Forcibly putting someone on the ground
  • verb
  • To use your arm to make something fly in the air
  • To move part of your body suddenly and forcefully
  • To confuse or upset someone
  • (E.g. judo) to forcibly put someone on the ground
  • To put something somewhere suddenly and roughly

stake

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US / steɪk /

UK / stek /

B1
  • noun
  • Share/interest in the success of a business, etc.
  • Money bet in a game that can be won or lost
  • The share you have in a company
  • Post stuck in the ground you can tie things to
  • verb
  • To bet or wager on an outcome
  • To risk something important by taking a risk

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

air

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US / eə(r) /

UK / er /

A1
  • noun
  • Mixture of gases around the earth that we breathe
  • A person's manner intended to impress others
  • verb
  • To expose to the outside, to dry or freshen
  • To broadcast a TV or radio show
  • To open a subject to discussion and debate

full

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US / fʊl /

UK / fʊl /

A1
  • adjecitve
  • Containing all the parts; complete
  • Containing or holding as much as possible
  • Having had enough food
  • adverb
  • In a direct manner; completely

hear

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US / hɪə(r) /

UK / hɪr /

A1
  • verb
  • To be aware of sound; to perceive with the ear
  • To be told or find out information or facts
  • To consider or listen to a court case

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

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

away

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US / ə'weɪ /

UK / əˈwe /

A1
  • adjecitve
  • Not present
  • adverb
  • Disappear completely
  • Doing something with a lot of energy
  • Not here; far from here; in a different direction
  • To a different area, location

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

mathematical

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US / ˌmæθə'mætɪkl /

UK / ˌmæθəˈmætɪkəl /

A2
  • adjecitve
  • Concerning numbers and equations

count

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US / kaʊnt /

UK / kaʊnt /

A2
  • noun
  • Number of things added together, e.g. votes
  • With the number of crimes, knockouts, as stated
  • verb
  • To add things together to find the total number
  • To matter or be important
  • To include someone or something in a final number

end

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US / end /

UK / ɛnd /

A1
  • noun
  • The point where a process or activity stops
  • A point that marks the limit of something; finish
  • Goal or desired result
  • The tip, edge or limit of something
  • verb
  • To be the last part of something

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

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

problem

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US / ˈprɒbləm /

UK / ˈprɑbləm /

A1
  • adjecitve
  • Causing trouble
  • noun
  • Something difficult to deal with or causes trouble
  • Question to show understanding of a math concept

whatsoever

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US / ˌwɒtsəʊ'evə /

UK / ˌhwɑtsoˈɛvɚ,ˌhwʌt-,ˌwɑt,ˌwʌt- /

B2
  • determiner
  • Used to add emphasis to an idea being expressed

cover

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US / 'kʌvə(r) /

UK / ˈkʌvɚ /

A1
  • noun
  • A different version of another song
  • Bed sheets; blankets
  • (Police or military) protection from attack
  • Amount of money to be paid in an insurance claim
  • Thing you put over something to close or hide it
  • Front and back part of a book or magazine
  • Shelter built to protect from the natural elements
  • verb
  • To record a different version of another song
  • To include as part of its area
  • To put something over something to hide it
  • To discuss a subject in a talk or meeting
  • To form a layer over something so it is hidden
  • To have sufficient funds to pay for something
  • To include something within an agreed limit
  • To report news on TV, radio or in a newspaper
  • (Police or military) to protect from attack
  • To travel a certain distance in a given time
  • To wrap something with something, such as a cloth

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

behave

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US / bɪˈheɪv /

UK / bɪˈhev /

A2
  • verb
  • To act correctly
  • To act in a particular way
  • To react in a particular way in a given case

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

win

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US / wɪn /

UK / wɪn /

A1
  • noun
  • Success in beating the other team or competitors
  • Success in a game or contest
  • verb
  • To get something as a prize because of a success
  • To gain something you want because of your efforts
  • To succeed in a game or contest

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

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

touch

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US / tʌtʃ /

UK / tʌtʃ /

A1
  • noun
  • Certain way of doing that makes something special
  • A small amount of something
  • Feeling of a surface
  • verb
  • To affect feelings, especially by causing sympathy
  • To be next to each other with no space between
  • To get involved with (used in negative)
  • To feel an object with your fingers, etc.

value

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US / 'vælju: /

UK / ˈvælju /

A1
  • noun
  • Importance you attach to something
  • Some information expressed as a number
  • Stated price of something; worth
  • verb
  • To place a high importance on something
  • To say how much money something is worth

case

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US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

enough

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US / ɪˈnʌf /

UK / ɪˈnʌf /

A1
  • adjecitve
  • Sufficient to answer the need
  • adverb
  • To a satisfactory degree
  • pronoun
  • Equal to what is needed; as much as required
  • Adequate number or amount

great

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US / ɡreɪt /

UK / ɡret /

A1
  • adjecitve
  • Very large in size
  • Very important
  • Very good; fantastic; wonderful
  • adverb
  • Very good; better than before
  • noun
  • Successful and well-admired person

tend

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US / tend /

UK / tɛnd /

A2
  • verb
  • To move or act in a certain manner
  • To take care of
  • To regularly behave in a certain way

guest

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US / ɡest /

UK / ɡɛst /

A2
  • adjecitve
  • Referring to people visiting or staying at a place
  • noun
  • Person invited to visit or stay in someone's home
  • Paying customer at a hotel or restaurant

hit

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US / hɪt /

UK / hɪt /

A1
  • noun
  • A planned killing, usually for money
  • Song, movie etc. that is successful
  • When someone strikes someone or something
  • Time when a player makes contact with the ball
  • Time when a website is accessed
  • verb
  • To have a negative impact on a person/place/thing
  • To press something, such as a button or switch
  • To suddenly realize the importance of something
  • To move your hand, a bat, etc. against with force
  • To fight, attack or damage something or someone
  • To arrive at a specific place, level, or goal
  • To make contact with the ball in a game or sport

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

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

tell

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US / tel /

UK / tɛl /

A1
  • verb
  • To (strongly) advise a person to do something
  • To be able to guess
  • To say or communicate information to someone
  • To inform, but without speaking; indicate
  • To have a negative effect on someone
  • To order someone to do something; command
  • To recognize something based on certain signs
  • To report something to an authority
  • To explain something or teach someone something

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

existence

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US / ɪɡ'zɪstəns /

UK / ɪɡˈzɪstəns /

A2
  • noun
  • State of being present, alive or real

happen

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US / 'hæpən /

UK / ˈhæpən /

A1
  • verb
  • To take place or occur

yeah

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US / jeə /

UK / ˈjɛə, ˈjæə, jɛ- /

A1
  • exclamation
  • Another way of saying 'yes'

banish

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US / 'bænɪʃ /

UK / ˈbænɪʃ /

B2
  • verb
  • To send someone away, often as punishment

clever

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US / 'klevə(r) /

UK / ˈklɛvɚ /

A1
  • adjecitve
  • Funny in a way that shows intelligence
  • Showing intelligence; quick to understand or learn

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

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

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

people

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US / 'pi:pl /

UK / ˈpipəl /

A1
  • noun
  • Persons sharing culture, country, background, etc.
  • Men, Women, Children

second

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US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

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

suppose

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US / sə'pəʊz /

UK / səˈpoʊz /

A2
  • conjunction
  • What if
  • verb
  • To imagine or guess what might happen

description

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US / dɪˈskrɪpʃn /

UK / dɪˈskrɪpʃən /

A2
  • noun
  • Explanation of what something is like, looks like

philosophically

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US / ˌfɪlə'sɒfɪklɪ /

UK / ˌfɪləˈsɑfɪkl:ɪ /

C1
  • adverb
  • In a calm, reasonable way, even if things are bad

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

decent

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US / ˈdi:snt /

UK / ˈdisənt /

B1
  • adjecitve
  • Being fairly good; acceptable

decision

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US / dɪ'sɪʒn /

UK / dɪˈsɪʒən /

A1
  • noun
  • Choice made after thinking; final judgment
  • Ability to make quick and confident choices

potentially

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US / pə'tenʃəlɪ /

UK / pəˈtɛnʃəlɪ /

B1
  • adverb
  • That could happen or become reality

really

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US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

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

expect

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US / ɪk'spekt /

UK / ɪkˈspɛkt /

A1
  • verb
  • To believe something is probably going to happen

sum

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US / sʌm /

UK / sʌm /

A2
  • noun
  • Amount when all is added together; total
  • verb
  • To add two or more numbers together; total

thin

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US / θɪn /

UK / θɪn /

A1
  • adjecitve
  • Flowing with ease; with a high percentage of water
  • (Of air) having little oxygen
  • Being or growing far apart in small amounts
  • Not thick; not wide in size
  • Having little flesh or fat on the body
  • Being weak or useless
  • verb
  • To make flow more easily by adding water or liquid

yet

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US / jet /

UK / jɛt /

A1
  • adverb
  • At a later time (used after ‘not’)
  • (Used to emphasize that thing is, will be greater)
  • Eventually; at a future time
  • Until now; up to the present
  • conjunction
  • Adding to what has been said, often as a contrast

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

good

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US / ɡʊd /

UK / ɡʊd /

A1
  • adjecitve
  • Proper, appropriate or right
  • (Of an amount) enough; plenty
  • Excellent; high quality
  • Acting well or properly; of moral character
  • In a positive or happy emotional state
  • noun
  • Advantage or benefit

single

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US / 'sɪŋɡl /

UK / ˈsɪŋɡəl /

A1
  • adjecitve
  • Being one only, without others
  • Only; merely
  • Not married or in a relationship
  • noun
  • One run in cricket or a hit baseball
  • An individual song from a CD or album
  • Person who is not married or in a relationship

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

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

carry

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US / ˈkæri /

UK / ˈkæri /

A1
  • verb
  • To have a child, be pregnant
  • To have a disease you might give to others
  • (Of stores) to sell a particular product
  • To hold something and move it to another place
  • To travel a long distance (sound)
  • To support the weight or burden of something

final

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US / ˈfaɪnl /

UK / ˈfaɪnəl /

A1
  • adjecitve
  • That will not be changed; permanent
  • Being the last thing in a series
  • noun
  • Last game in a series in a competition

same

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US / seɪm /

UK / sem /

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

somebody

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US / 'sʌmbədɪ /

UK / ˈsʌmˌbɑdi, -ˌbʌdi, -bədi /

A1
  • noun
  • Important well-respected person
  • pronoun
  • Person who is not known or named

fix

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US / fɪks /

UK / fɪks /

A2
  • noun
  • Answer to a problem
  • verb
  • To arrange or prepare something
  • To attach something so it will not move or change
  • To dishonestly arrange the result of a game
  • To make an animal unable to produce young
  • To make something whole or able to work again

infinitely

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US / ˈɪnfɪnətli /

UK / ˈɪnfənɪtlɪ /

B2
  • adverb
  • Continuing forever without end; very great

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

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)

quite

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US / kwaɪt /

UK / kwaɪt /

A1
  • adverb
  • Not very; fairly
  • Very; In a complete or total manner

size

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US / saɪz /

UK / saɪz /

A1
  • noun
  • How big or small a thing is
  • Standard measurements for clothing, shoes
  • verb
  • To make something to fit a particular measurement
  • To organize or group from small to large

whole

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US / həul /

UK / hol /

A1
  • adjecitve
  • Complete or full; all of
  • Being in a good condition
  • noun
  • Complete amount or sum; total

any

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US / 'enɪ /

UK / ˈɛni /

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

anybody

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US / ˈenibɒdi /

UK / ˈenibʌdi /

A1
  • pronoun
  • Any person; anyone

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

game

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US / ɡeɪm /

UK / ɡem /

A1
  • noun
  • Activity with rules that people play to have fun
  • Birds and animals people hunt to kill and eat
  • Match between two teams

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

ban

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US / bæn /

UK / bæn /

B1
  • noun
  • Official action preventing something happening
  • verb
  • To make something illegal or not allowed

most

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US / məʊst /

UK / most /

A1
  • adverb
  • Very; extremely
  • Greatest possible degree
  • pronoun
  • Nearly all of something

name

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US / neɪm /

UK / nem /

A1
  • noun
  • What something or someone is called
  • verb
  • To state what someone is called, e.g. John

rather

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US / 'rɑ:ðə(r) /

UK / ˈræðɚ, ˈrɑðɚ /

A1
  • adverb
  • Somewhat; fairly; not that much

paint

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US / peɪnt /

UK / pent /

A1
  • noun
  • Colored liquid you apply with a brush
  • verb
  • To make a picture with colored liquids
  • To describe as
  • To apply a color, oil or sealant with a brush

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

double

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US / 'dʌbl /

UK / ˈdʌbəl /

A2
  • adjecitve
  • Concerning or intended for use by two people
  • Two times the amount or degree; twice
  • Made of two parts that are the same, similar
  • noun
  • Person that is exactly like someone else
  • verb
  • To be used for two functions at the same time
  • To make or become twice as much

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

trick

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US / trɪk /

UK / trɪk /

A2
  • adjecitve
  • Not reliable; likely to deceive you
  • noun
  • Act of trying to fool someone
  • Quick or skillful way of doing something
  • Something done to make someone laugh
  • verb
  • To fool someone in order to obtain a result
  • To playfully tease or fool to make someone laugh

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

completely

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US / kəmˈpli:tli /

UK / kəmˈpliːtli /

A1
  • adverb
  • In every way or as much as possible

connection

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US / kəˈnekʃn /

UK / kəˈnɛkʃən /

A2
  • noun
  • Something that joins things together; being joined
  • Person you know who can help you in some way
  • Changing vehicles when traveling

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

perhaps

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US / pəˈhæps /

UK / pɚˈhæps /

A1
  • adverb
  • Possibly, but not certainly; maybe

put

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US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

ten

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US / ten /

UK / tɛn /

A1
  • number
  • 10

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

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

money

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US / 'mʌnɪ /

UK / ˈmʌni /

A1
  • noun
  • Coins or notes we use to pay for things

centre

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US / ˈsentə(r) /

UK / ˈsɛntɚ /

A1
  • noun
  • Community place people go health or social reasons
  • Place in the middle of something
  • Person or thing that is attracting attention
  • verb
  • To place a focus on something

from

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US / frəm /

UK / frʌm, frɑm,frəm /

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

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

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

arise

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US / əˈraɪz /

UK / əˈraɪz /

A2
  • verb
  • To stand up
  • To result or happen due to a particular event

real

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US / rɪəl /

UK / ˈriəl, ril /

A1
  • adjecitve
  • Actually existing or happening, not imagined
  • Being important or special

sometimes

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US / ˈsʌmtaɪmz /

UK / ˈsʌmˌtaɪmz /

A1
  • adverb
  • Only at certain times; occasionally

big

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US / bɪɡ /

UK / bɪɡ /

A1
  • adjecitve
  • Popular
  • Serious
  • Large

fit

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US / fɪt /

UK / fɪt /

A2
  • adjecitve
  • Good looking; physically attractive
  • Proper or acceptable; morally or socially correct
  • noun
  • Sudden loss of body control; attack (of crying)
  • verb
  • To install a machine, equipment etc.
  • To adjust or change to the right size or shape
  • To be the right size and shape that you want

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

natural

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US / ˈnætʃərəl /

UK / ˈnætʃərəl, ˈnætʃrəl /

A1
  • adjecitve
  • Being as one would expect; being usual or normal
  • Not made by humans; without human intervention

person

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US / 'pɜ:sn /

UK / 'pɜ:rsn /

A1
  • noun
  • Man, woman or child

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

dart

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US / dɑ:t /

UK / dɑ:rt /

B1
  • verb
  • To move suddenly away; race away

fair

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US / feə(r) /

UK / fɛr /

A1
  • adjecitve
  • Neither very good nor very bad; average
  • (Of skin) light colored; not dark
  • Quite good; quite a lot
  • Treating all people the same way
  • (Of hair) light colored; blonde
  • (Of weather) sunny; not raining
  • noun
  • Event for companies to show their products
  • Event to sell things to help a charity

forward

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US / 'fɔ:wəd /

UK / ˈfɔrwəd /

A1
  • adjecitve
  • Toward what is ahead; in front
  • Acting in a socially aggressive manner; pushy
  • adverb
  • Toward the front in place; in front
  • Toward a future time; to a more advanced state
  • verb
  • To send something to another address or person

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

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

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

turn

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US / tɜ:n /

UK / tɚn /

A1
  • noun
  • Place where changing of direction happens
  • Your time or chance to perform a duty
  • Your chance to play or do in say a game
  • Unexpected change, as in the weather
  • verb
  • To become (a particular age)
  • To become a different quality, color, etc.
  • To change the direction of something, e.g. a car
  • To move in an opposite direction or position
  • To shape metal with a spinning tool

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

three

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US / θri: /

UK / θri /

A1
  • number
  • Number 3

surface

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US / 'sɜ:fɪs /

UK / ˈsɚfəs /

A2
  • adjecitve
  • Of the top layer; not deep or meaningful
  • noun
  • Top layer of the ground or of water
  • Nature or emotions that show, but may not be true
  • Outside or upper layer of something
  • verb
  • To give (road) a top layer
  • To appear after being hidden, unseen, or unknown
  • To come to the top of something; emerge
  • To come to the top level of water, mud, etc.

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

price

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US / praɪs /

UK / praɪs /

A1
  • noun
  • Person's name
  • Cost of something in money
  • verb
  • To determine or set the cost of something

clash

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US / klæʃ /

UK / klæʃ /

B1
  • noun
  • A conflict; disagreement
  • verb
  • To have a disagreement or fight over something
  • (Of colors) to not suit or match appealingly

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

run

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US / rʌn /

UK / rʌn /

A1
  • noun
  • Journey between two places made by ship or car
  • Series of similar things or successes and failures
  • Act of running; exercise of running
  • verb
  • To depart or travel according to a schedule
  • To cause an animal to move in a certain direction
  • (Of an engine) to be operating
  • To start or use a computer program
  • To flow in a certain direction, like a liquid
  • To manage or operate a business
  • To operate or drive something
  • (Of a road) to go from one place to another
  • To move your legs faster than walking

also

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US / 'ɔ:lsəʊ /

UK / ˈɔlso /

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

fine

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US / faɪn /

UK / faɪn /

A2
  • adjecitve
  • Good, acceptable or satisfactory
  • Of high quality; made with great skill
  • In a careful or exact manner; into small pieces
  • Being of high quality
  • Good; okay; no problem
  • (Of weather) good; not raining
  • noun
  • Money you have to pay because you broke a rule
  • verb
  • To pay money because you broke a law

kind

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US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

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)

sensible

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US / ˈsensəbl /

UK / ˈsɛnsəbəl /

A2
  • adjecitve
  • Able to judge something reasonably or fairly
  • Being useful/practical rather than fun/fashionable

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

answer

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US / 'ɑ:nsə(r) /

UK / ˈænsɚ /

A1
  • noun
  • Reply to a question someone asks
  • Solution to a problem or test question
  • verb
  • To reply to a question someone asks
  • To solve a test question or a problem

filter

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US / 'fɪltə(r) /

UK / ˈfɪltɚ /

B1
  • noun
  • Device to remove certain types of light, sound
  • Device to remove unwanted things from liquid, gas
  • verb
  • To remove certain types of light, sound
  • To remove unwanted substances from a liquid or gas

flip

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US / flɪp /

UK / flɪp /

B2
  • noun
  • Act of turning your body in the air; somersault
  • Movement of something from one position to another
  • verb
  • To turn your body in the air, as in gymnastics
  • To move into a different position quickly
  • To move a button or switch to turn on or off

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

rational

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US / 'ræʃnəl /

UK / ˈræʃənəl /

A2
  • adjecitve
  • Able to think clearly

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

area

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US / 'eərɪə /

UK / ˈɛriə /

A1
  • noun
  • Amount of measured space
  • A specific section or space; part of a region
  • A subject or field of study

somehow

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US / ˈsʌmhaʊ /

UK / ˈsʌmˌhaʊ /

A1
  • adverb
  • In a way that is not known or certain

taper

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US / 'teɪpə(r) /

UK / ˈtepɚ /

B2
  • verb
  • (Of e.g. streets) to become gradually narrower

pot

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US / pɒt /

UK / pɑt /

A2
  • noun
  • Container designed to hold or store something
  • Deep, round container that is used for cooking
  • Large, significant quantity of something
  • Slang name for marijuana
  • Net pocket at the corners, etc. of a snooker table
  • Money that can be won in a card game or a bet
  • verb
  • To plant something in a container filled with soil
  • To hit a ball into a table pocket in snooker

weird

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US / wɪəd /

UK / wɪrd /

B1
  • adjecitve
  • Odd or unusual; surprising; strange

puzzle

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US / 'pʌzl /

UK / ˈpʌzəl /

A2
  • noun
  • Something challenging to explain or understand
  • Game requiring the player to find an answer
  • Game with many pieces, e.g. forming a picture
  • A problem requiring thought and skill to be solved
  • verb
  • To be a challenge to understand; confuse

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

after

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US / 'ɑ:ftə(r) /

UK / ˈæftɚ /

A1
  • adverb
  • Later than another time, or behind something
  • conjunction
  • Following something before
  • preposition
  • When an event happened or time has passed

enclose

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US / ɪnˈkləʊz /

UK / ɪnˈkloʊz /

B1
  • verb
  • To place something in a package or envelope
  • To surround something

guess

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US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

many

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US / 'menɪ /

UK / ˈmɛni /

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

relate

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US / rɪ'leɪt /

UK / rɪˈlet /

A2
  • verb
  • To demonstrate a logical relationship between
  • To understand or sympathize with, e.g. a problem
  • To tell a story, or tell about a particular event

trumpet

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US / ˈtrʌmpɪt /

UK / ˈtrʌmpɪt /

B2
  • noun
  • Brass wind instrument with a flared bell
  • Device for making sound louder
  • Sound like that made by a trumpet
  • verb
  • To make a sound like a trumpet
  • To praise (someone's achievement, often your own)

surely

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US / ˈʃʊəli /

UK / ˈʃʊrli /

A1
  • adverb
  • With certainty; definitely

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

tail

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US / teɪl /

UK / tel /

A2
  • noun
  • Extended part at the back of an animal's body
  • Back or last part of something e.g. shirt
  • verb
  • To be end of (a march or parade, line)
  • To follow someone secretly and watch what they do

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

four

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US / fɔ:(r) /

UK / fɔr, for /

A1
  • number
  • 4

inside

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US / ˌɪn'saɪd /

UK / ɪnˈsaɪd, ˈɪnˌsaɪd /

A2
  • adjecitve
  • Being in something
  • Being in a building
  • adverb
  • Into a house; indoors
  • noun
  • Inner part or surface of something

once

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US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

satisfy

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US / ˈsætɪsfaɪ /

UK / ˈsætɪsˌfaɪ /

A2
  • verb
  • To make someone happy because they got their wish
  • To do what is required in order to finish

bus

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US / bʌs /

UK / bʌs /

A1
  • noun
  • A large road vehicle used for carrying many people
  • verb
  • To move people by coach or bus

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

third

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US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

sure

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US / ʃʊə(r) /

UK / ʃʊr /

A1
  • adjecitve
  • Having no doubts about something
  • Have confidence in your own words or actions
  • Firmly established or held; being firm or stable
  • Being correct or true
  • adverb
  • What you say to agree willingly

shift

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US / ʃɪft /

UK / ʃɪft /

A2
  • adjecitve
  • (Of work) starting at a certain time, as at night
  • noun
  • A change in a persons plans, opinions or beliefs
  • Period of work starting at a certain time
  • verb
  • To change in position or direction
  • To move something from one place to another

should

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US / ʃʊd /

UK / ʃʊd /

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

sort

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US / sɔ:t /

UK / sɔrt /

A1
  • noun
  • Group or class of similar things or people
  • verb
  • To organize things by putting them into groups
  • To deal with things in an organized way

coin

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US / kɔɪn /

UK / kɔɪn /

A1
  • noun
  • A small, flat piece of metal used as money
  • verb
  • To make coins from metal
  • To invent a new word that becomes popular

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

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

small

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US / smɔ:l /

UK / smɔl /

A1
  • adjecitve
  • Little in size; not big
  • (Of letters) not written in capital letters
  • Being insignificant or minor
  • (Of a business) with few people or things; local
  • (Of voice) being soft and quiet
  • (Of a child) being young

thick

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US / θɪk /

UK / θɪk /

A2
  • adjecitve
  • Difficult to see through, as fog
  • Full of (people, etc.)
  • (Of a liquid) that moves or pours slowly
  • Stupid; not smart
  • (Of person's accent) hard to understand
  • Having a large distance between two surfaces

crumble

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US / ˈkrʌmbl /

UK / ˈkrʌmbəl /

B2
  • verb
  • To break into small parts or crumbs

rich

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US / rɪtʃ /

UK / rɪtʃ /

A1
  • adjecitve
  • Having a lot of money or valuable possessions
  • Containing a lot of exciting events or experiences and therefore very interesting
  • (of a color, sound, smell, etc.) Pleasantly deep or strong
  • If food is rich, it contains a large amount of oil, butter, eggs, or cream.

home

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US / həʊm /

UK / hom /

A1
  • adjecitve
  • A sports team's own field or place of play
  • adverb
  • Into the correct or intended position
  • noun
  • House, apartment or building to be rented or sold
  • Institution for sick or elderly people
  • Place where a person or a family lives
  • Country where a person lives or was born
  • Region that is native to peoples, plant or animals
  • verb
  • To move towards a particular target location

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

somewhere

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US / 'sʌmweə(r) /

UK / ˈsʌmˌhwɛr, -ˌwɛr /

A1
  • adverb
  • At or to an unknown or unnamed place

talk

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US / tɔ:k /

UK / tɔk /

A1
  • noun
  • Style of speaking
  • Discussion between two countries
  • Giving information in front of people; lecture
  • Saying things or ideas to someone with words
  • verb
  • To make a formal speech about something
  • To say things or ideas to someone with words

amount

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US / ə'maʊnt /

UK / əˈmaʊnt /

A1
  • noun
  • Quantity of something
  • verb
  • To add up to a certain figure

difference

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US / 'dɪfrəns /

UK / ˈdɪfərəns, ˈdɪfrəns /

A1
  • noun
  • A thing or issue that people do not agree about
  • Not of the same kind; unlike other things

head

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US / hed /

UK / hɛd /

A1
  • noun
  • Counter for the number of cattle
  • Natural mental ability or intelligence
  • Leader or person with the greatest authority
  • Mind; mental ability; mental state
  • Side of a coin with a head on it
  • Top part of your body with eyes and a mouth
  • Starting point of something, e.g. a river
  • verb
  • To hit a ball with your head in a game
  • To be first or at the front or top (e.g. a list)
  • To travel or move toward a particular place; To go in a particular direction
  • To become the leader of something
  • To lead or be responsible for something

never

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US / 'nevə(r) /

UK / ˈnɛvɚ /

A1
  • adverb
  • Not ever; not at any time

reception

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US / rɪˈsepʃn /

UK / rɪˈsɛpʃən /

B1
  • noun
  • Front desk area of an organization or building
  • Party occurring after an event it celebrates
  • Quality of radio or television signals
  • Act of receiving something in a particular way

object

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US / 'ɒbdʒɪkt /

UK / ˈɑbdʒɪkt /

A2
  • noun
  • Something you can see or touch, but is not alive
  • Goal or purpose of a particular plan or activity
  • The thing that the action of a verb acts upon
  • verb
  • To disagree; to protest against an idea or plan

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

granular

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US / ˈgrænjələ(r) /

UK / ˈɡrænjəlɚ /

C1
  • adjecitve
  • Composed of or covered with grain

math

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US / mæθ /

UK / mæθ /

A2
  • noun
  • Study or science of numbers and shapes

molecule

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US / ˈmɒlɪkju:l /

UK / ˈmɑlɪˌkjul /

B2
  • noun
  • Two or more atoms chemically combined

stuff

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US / stʌf /

UK / stʌf /

A1
  • noun
  • Generic description for things, materials, objects
  • verb
  • To push material inside something, with force

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

dartboard

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US / ˈdɑːtbɔːd /

UK / ˈdɑːrtbɔːrd /

A1
  • other
  • A circular board of wood or cork used as the target in the game of darts

fact

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US / fækt /

UK / fækt /

A1
  • noun
  • Something that is known or proved to be true

few

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US / fju: /

UK / fju /

A1
  • pronoun
  • Not many, a small number

much

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US / mʌtʃ /

UK / mʌtʃ /

A1
  • adjecitve
  • Very; to a high level or degree
  • adverb
  • A lot; large amount; a high degree of
  • Nearly; basically
  • On many occasions; often
  • noun
  • A large amount; a great quantity

probability

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US / ˌprɒbəˈbɪləti /

UK / ˌprɑ:bəˈbɪləti /

A2
  • noun
  • What the chances are that something will happen

winning

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US / ˈwɪnɪŋ /

UK / ˈwɪnɪŋ /

A1
  • verb
  • To gain something you want because of your efforts
  • To succeed in a game or contest

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

infinity

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US / ɪn'fɪnətɪ /

UK / ɪnˈfɪnɪti /

B2
  • noun
  • State of being without end; endless time, space

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

why

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US / waɪ /

UK / hwaɪ, waɪ /

A1
  • adverb
  • Question word to ask for a reason
  • exclamation
  • (Used to express surprise or approval)

ask

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US / ɑ:sk /

UK / æsk /

A1
  • verb
  • To say to someone that you want something

exact

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US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

land

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US / lænd /

UK / lænd /

A1
  • noun
  • Region or country
  • Earth; the ground
  • verb
  • To arrive or cause a boat to arrive at the shore
  • To obtain or get something that you wanted
  • To (cause to) come down to the ground safely
  • To cause to arrive in a specific place or state

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

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

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears
  • Introduction to Video Content
  • The video titled 'Infinity Paradoxes - Numberphile' discusses four paradoxes that revolve around the concept of infinity. The first paradox introduced is known as the Hilbert Hotel. In this scenario, there is a hotel with an infinite number of rooms, all of which are currently occupied. A new guest arrives at the reception desk, and despite the hotel appearing to be full, the manager comes up with a clever solution. The manager shifts each guest to the next room, creating a vacancy in room number one. The new guest is then assigned to this room. This process can be repeated infinitely, allowing an infinite number of new guests to be accommodated. This paradox challenges our intuition about how full hotels operate and highlights the unique properties of infinity. The absence of a final room in the infinite hotel demonstrates that infinity is a fascinating concept that defies traditional notions of finitude. The second paradox discussed in the video is Gabriel's trumpet, but the details of this paradox are not provided in the subtitles.
  • Subtitles section
  • We're going to talk about four paradoxes that touch on the topic of infinity.
  • First one, we've got the Hilbert Hotel.
  • This is a hotel with infinitely many rooms, and at the moment there's somebody in every single room.
  • So it's a full hotel, and then a new customer rolls up at the reception desk.
  • Now you might think they've got to turn them away because the hotel's full, but the manager's clever.
  • And here's what he does.
  • He shifts the person in room one to room two, and the person in room two to room three, and the person in room three to room four, and so on.
  • Everyone gets shifted forward one room.
  • Because there's infinitely many rooms, you never run out of rooms to put people in.
  • And when you've done all of this, room one's free, so the new guest gets put in room number one.
  • So you can fit in a new guest.
  • You could fit in two new guests.
  • You could fit in ten new guests.
  • And even if an infinite bus of new customers rolls up, you can fit them all in.
  • I guess it's that when I first heard the description, I thought, well, that hotel's full.
  • You can't fit anybody in it.
  • That's how full hotels work.
  • But then once you're shown that you can fit as many new people in the hotel as you like, you learn something new about infinity.
  • So your intuitions change.
  • And the trick is, because it's an infinite hotel, there is no final room.
  • If there were a final room, you could count all the rooms, and there wouldn't be infinitely many of them.
  • I think he's using the idea to say, you know, infinity's interesting.
  • It's philosophically interesting, because you might have thought things went like this, but they don't.
  • And we can show mathematically that they don't.
  • Paradox number two.
  • This is the paradox of Gabriel's trumpet.
  • So the idea is we have this mathematical shape, this mathematical object.
  • And it's shaped like a trumpet.
  • It'll start off here, and it'll taper and get thinner and thinner and thinner and thinner and thinner.
  • And it tends off to infinity, getting thinner and thinner all the way.
  • So that mathematical object has an infinite surface area, but the volume it encloses, the air in the centre of the trumpet, is only a finite volume.
  • Suppose you were told you had to paint the inside of that trumpet.
  • Well, on the one hand, you've got to paint an infinitely big surface, so you're going to need an infinite bucket of paint.
  • But on the other hand, you could just take a finite, big enough can of paint, tip it into the trumpet, and let it filter its way down.
  • So it looks like you only need a finite amount of paint to paint an infinite surface area.
  • That's really, really strange.
  • If we're thinking about real physical paint, you just can't paint the whole surface, because it gets so thin at one end that you're just not going to fit the paint down there.
  • So I guess the clash arises when we think about the difference between the mathematical idea of a surface and the physical idea of paint, which is real, thick stuff.
  • If we had mathematical paint where the molecules had no size whatsoever, it looks like you need an infinite amount of that to cover that infinite surface area.
  • He thought there was something really strange going on here.
  • He gave lots of proofs of this idea, because I think at first he thought he'd made a mistake.
  • Lots of mathematicians thought that there was something wrong with the idea of infinity, that maybe somehow we should banish infinity, because puzzles like this clash.
  • They show there's something wrong with the idea, so we should somehow ban it from our mathematics.
  • But in fact, infinity works just fine in mathematics, but we have to sometimes change our ideas about how the world works to fit it in.
  • Number three.
  • So this is the puzzle of the dartboard.
  • So we suppose we've got a dartboard, and we've got a dart, and we're going to throw the dart at the dartboard.
  • And let's just suppose we're guaranteed 100% chance to hit the dartboard.
  • And then we ask the question, think about the exact centre point of the dart.
  • And we think about an exact point, a mathematical point on the dartboard.
  • And we ask the question, what's the chance our dart is going to hit that exact point?
  • And it turns out we can't give a sensible answer.
  • So suppose on the one hand that we say it's got a chance greater than zero of hitting that point.
  • Well, there's a problem with that.
  • If it's got a greater than zero chance of hitting that point, the same goes for every other point on the dartboard.
  • And there's infinitely many of them.
  • In fact, there's a big infinity of those mathematical points.
  • When we add all those chances together to give us the chance that the dart's going to hit the dartboard at all, we end up with an infinite probability.
  • We can't have an infinite probability.
  • You can't get a probability bigger than one that something will happen.
  • OK, so we've got a problem with the idea that the chance of the dart hitting that point is bigger than zero.
  • So on the other hand, what happens if the chance is zero?
  • Well, that's also strange, because if the chance of hitting that point is zero, we could say the same for every point.
  • So the chance of hitting any point on the dartboard is zero.
  • It's not going to happen.
  • But that's really strange, because we're sure the dart's going to hit the dartboard somewhere.
  • Again, one thing philosophers say about this is the idea of banning infinity.
  • So we say, don't think about the exact mathematical point of the dart.
  • We think about an area.
  • Any real physical dart has an area at its centre.
  • And we think about what's the chance that it hits an area on the dartboard.
  • And then we divide these up in a finite way, and the problem goes away.
  • As the area gets bigger, the probability that the dart hits there is bigger.
  • As it gets smaller, the probability that the dart hits there gets smaller.
  • So it's this kind of granular nature of our existence that gets us out of trouble.
  • Yeah, that's right.
  • So if everything that we think about is an area rather than an exact point, the problem goes away.
  • But that's not completely satisfying.
  • After all, we can think of an area getting smaller and smaller and smaller and tending to infinity.
  • Shouldn't we have a decent answer to this problem when we get to the infinite case?
  • And, you know, maybe we don't have a very good answer to it.
  • OK, so here's the fourth paradox.
  • This is perhaps the most interesting one of them all because it relates to what rational humans should do in betting games.
  • You go to a casino, and they put a pound in the pot.
  • And they say, we're going to flip a fair coin.
  • And when it lands on the tail, you get whatever's in the pot.
  • If we flip a head, the casino doubles what's in the pot.
  • And we play again.
  • If it gets a tail, you get what's in the pot.
  • If it's a head, they double the pot.
  • And we carry on playing.
  • And then they ask you the question, how much would you pay to get into this game?
  • Name your price.
  • You've got to pay something to play.
  • What would you pay?
  • And I think most people think about this a bit and say something like maybe a few pounds.
  • Maybe if you're rich, you'd say 20 pounds.
  • The mathematical theory, on the other hand, tells you bet whatever you've got.
  • Stake any amount of money you can get your hands on on this game.
  • Because the expected winnings is infinite.
  • Your expected take-home is infinite if you play the game.
  • So the way we work out the expected take-home winnings is we look at each case.
  • If you flip a tail on the first go, how much would you win?
  • Added to if you flip a tail on the second go, how much would you win?
  • Added to if you flip a tail on the third go, how much would you win?
  • And we sum all of these.
  • But because the game hasn't got a fixed end point, we sum infinitely many of these.
  • And in fact, the expected value of each play of the game is 1⁄2.
  • So we're adding 1⁄2 to 1⁄2 to 1⁄2 to 1⁄2 infinitely many times.
  • That's why the expected value of what you'll take home is infinitely big.
  • But we wouldn't bet our house, would we?
  • We wouldn't bet everything.
  • I wouldn't, and I don't think you would.
  • What does that say?
  • I think it says something interesting about us.
  • Perhaps it says that we're more risk-averse than the mathematical theory would have us believe.
  • Perhaps it says that the value of money changes the more you accrue.
  • Perhaps it says something else that we haven't quite worked yet, that we should figure into what makes us rational reasoners, that we haven't yet taken account of in the maths.
  • You're sort of saying that as if humans are wrong to not bet everything on it.
  • But surely if humans did that, casinos would set that game up and own all their houses by now.
  • Well, good point.
  • To make the maths come out, the casino has to guarantee, so you have to know in advance, that they will bet as much as they need.
  • So there would have to be a casino with an infinite amount of money, potentially, to put into this game.
  • So one way out of it is to say, look, there's no casino with that amount of money, and if we say after X amount of money has been put in the pot, that's it, that's all the casino can do, then the numbers change and it turns out you'd be irrational to put lots of money into it.
  • We have this mathematical theory of rational decision making.
  • Most mathematical theories don't crumble when you put infinity in.
  • They work just fine.
  • So why is it that theories about us, how we should or shouldn't behave, go really weird when you put infinity in?
  • So suppose we take all the natural numbers together.
  • None of those are infinitely big.
  • Each one is a finite number, but there's infinitely many of them.
  • So if we were asked to count them, we'd say there's an infinite connection.