Shadowing Practice: WHAT ARE NATURAL NUMBERS? - Learn English Speaking with Video
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Hello, welcome back to another video.
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I would like you to know today what the properties of numbers are.
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Okay?
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I know we all use numbers every day, but do you know what real numbers are?
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Do you know what a natural number is?
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If a number is not natural, what would you say it is?
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Unnatural or supernatural?
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Well, let's find out.
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so properties of numbers i'm just going to
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start with what i just asked natural numbers
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if a number is natural it means you can find it in nature
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and when humans try to count or try to talk about numbers They do this a lot.
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One, two, three.
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See the first number?
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That's the first natural number.
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One.
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Not zero.
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There's no zero among natural numbers.
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So the set of natural numbers are the numbers you can count on your fingers.
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One, two, three, four, five.
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All numbers are positive.
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So if you want to know natural numbers, you just need to look at your fingers.
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Whatever you find is a natural number.
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Okay, so set of natural numbers will be positive one, positive two, like that, three, four, all the way to the end.
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Don't stop.
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If it's a natural number, it keeps on going forever and ever.
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Okay, let's go to number two.
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So if a number is not a natural number, what is it?
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It must be on the other side of the negative.
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Okay, so, but before you cross to the other side of the negative, there's a number just before positive 1.
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That number is called 0.
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0 is not a natural number, but it belongs to the set of numbers called whole numbers.
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So, our next definition is the set of whole numbers.
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If a number is a whole number, well it is either a natural number or it's a zero.
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Zero plus the set of natural numbers.
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I love this!
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numbers
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so it's a whole numbers are just natural numbers including zero
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that's it that's all we got to say let's move on to the next set let's talk about integers
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why am I writing like this?
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Come on.
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Integers.
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Okay, what are integers?
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Well, integers are all these things you've seen.
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Whole numbers plus whole negative.
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I don't want to say negative whole numbers, but if that's how you're going to understand it,
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Oh, let's say they are whole numbers plus all negative.
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Oh, there's no negative natural number.
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Just know if we change these signs to negative, just look at your number line.
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Okay?
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You walk into a classroom, you see the number line from negative infinity to zero to positive infinity.
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That's what you call integers.
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Put that in your head.
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I'm just going to write the number line from left to right.
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no fractions no decimals we don't call them whole numbers
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but they are whole numbers
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but still have negative portion of the whole that's confusing just
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stick to it just look at the number line all the numbers you see are what you call integers keep
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that in your head or in your notebook
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and then later in your head let's move on the next thing let's go to real numbers whoa
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so real numbers are real okay
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if a number is a real number it means it is any of these things
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that you've known or maybe fractions decimals rational or irrational numbers just know
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that every number you know is a real number unless there's a part of it
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that is not real
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and the part of a number is not real you say it is an imaginary number
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or a complex number i'm going to explain what an imaginary number is
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or what a complex number is but just know
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that every number you know is real all numbers fractions decimals
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whole numbers negative positive zeros infinity All those numbers are real, okay?
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Real numbers.
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All numbers that are not imaginary.
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Okay?
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So, if a number is not imaginary, it's a real number.
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This is the largest group of numbers you'll be dealing with, okay?
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So if a number is not real, it's going to be imaginary.
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Now what's an imaginary number?
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That's the next thing I'm going to do.
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Let's get rid of this.
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I know this is in your head already.
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Let's go.
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Come on.
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So, what's an imaginary number?
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Imaginary number.
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Let me give you a simple example.
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The square root of 4 is positive 2.
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Because positive 2 times positive 2 is going to give you 4.
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So the root of 4 is going to be 2.
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Now let's look at, what if I said that the square root of 4 is negative 2?
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Will I be correct?
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Yes, I will be because negative 2 times negative 2 is still going to be positive 4.
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So, what if I say the square root of negative 4?
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And that becomes impossible because it cannot be negative 2 and it cannot be positive 2
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because both of these are answers to square root of 4.
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So what's the square root of negative 4?
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Yeah, it's a bit twisted.
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What if we rewrite this as the square root of negative 1 multiplied by 4?
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Negative 1 multiplied by 4 gives you the square root of negative 1 multiplied by the square root of 4.
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Ah, now we can come back to getting our answer positive to or negative to whatever we choose,
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will be fine but what again is the square root of negative one it is not one
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and it is not negative one
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because those two numbers multiply negative one times negative one gives you one not negative one
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so how do we resolve this well we just need to imagine
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that there is an answer is it real no that's why it's called an imaginary number
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so this is called the imaginary portion of the answer and it is written as i.
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The square root of 4 is 2.
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So our answer here is 2i or negative 2i, depending on which of these options you pick.
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However, the i is there.
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That i means imaginary.
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Okay?
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So if a number doesn't have this kind of behavior, you know the number is real.
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If it has an I in it, it's imaginary.
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Now you know your sets of numbers, you know the properties of numbers.
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There's some other properties that you should know by now.
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You should know what an even number is.
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You should know what an odd number is.
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And you should know what a prime number is.
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Okay?
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You should know what a fraction is.
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and you should know what a decimal is, and then all kinds of decimals,
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but ultimately you should know what a rational number is.
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That would be my final point.
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Rational numbers.
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Rational numbers a number is rational
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if it can be written as a
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fraction rational numbers are all numbers
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that can be written
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as a fraction let me change this
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so the grammar is correct it's any number any number any number
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that can be written as a fraction
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so every number we've talked about today is supposed to be
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a part well all rational numbers will be real numbers
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so what's a rational number well all integers
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or whole numbers all those things can be written as a
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fraction for example three is the same thing as three over one well there's some few numbers
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that are not rational the most popular of them will be
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so will be pi so just know
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that every number you come across is supposed to be rational unless it has a behavior like this
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when you write it in decimal
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or as a you can't write it as a fraction
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so you have to write as a decimal and
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when you write it as a decimal it does not repeat
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okay it does not it behaves like pi this is a good example of an irrational number okay
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so pi is irrational because
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when you start writing the digits of pi it has no
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end that's number one another good example is the square root of any number
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that is not a perfect square or the cube root of any number
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that is not a perfect cube or the fourth root of any number
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that is not a perfect fourth okay so
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if you try to take the square root of say eight
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for example well this eight is not a perfect square you can't really tell
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so when you write the answer you're going to have decimals
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that keep on going you can check it in your calculator
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so the square root of a is also irrational okay
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and there's some other mathematical constants
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that you never find them um to end there's no you just approximate you just approximate you just approximate
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or you assume a fraction which is not real
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so pi is irrational the square root of a number
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that is not a perfect square is also irrational okay i
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believe you've learned something you've gotten gotten something to keep okay
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if you ever forget any of these things come back to
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the video okay send me an email send me uh put
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a comment in the description um in the comment section
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and please share like
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and subscribe to my channel it encourages me to put up more videos thank you
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and don't stop learning god bless you bye Thank you.
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Woordenschat en spreektips bij deze les
Deze spreekles op niveau B1 is gebaseerd op de video “WHAT ARE NATURAL NUMBERS?”. Deze woorden komen het vaakst terug: negative, root, square, natural, imaginary. Deze video bevat 166 zinnen en 1559 woorden om na te spreken. Het gesproken deel duurt 12:03. De spreker praat in een gelijkmatig tempo van ongeveer 129 woorden per minuut, prettig om te shadowen. 88% van de woorden hoort bij de 3.000 meest gebruikte Engelse woorden, dus de woordenschat is goed te volgen.
Belangrijke woorden in deze video
De 15 moeilijkste woorden uit de video, met uitspraak en betekenis:
| Woord | Uitspraak | Betekenis |
|---|---|---|
| imaginary bijvoeglijk naamwoord | /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/ | denkbeeldig, ingebeeld |
| fraction zelfstandig naamwoord | /ˈfɹæk.ʃən/ | fractie |
| rational bijvoeglijk naamwoord | /ˈɹæʃ(ə)nəl/ | rationeel, redelijk |
| decimal zelfstandig naamwoord | /ˈdɛs.ɪ.məl/ | decimaalstelsel, tientallig talstelsel |
| integer zelfstandig naamwoord | /ˈɪn.tɪ.d͡ʒə(ɹ)/ | geheel getal |
| irrational bijvoeglijk naamwoord | /ɪˈɹæʃ.(ə.)nəl/ | irrationeel, irrationele |
| multiply werkwoord | /ˈmʌltɪplaɪ/ | vermenigvuldigen |
| approximate bijvoeglijk naamwoord | /əˈpɹɑk.sə.mət/ | benaderend |
| infinity zelfstandig naamwoord | /ɪnˈfɪnɪti/ | oneindigheid |
| cube zelfstandig naamwoord | /kjub/ | kubus, regelmatig zesvlak |
| rewrite werkwoord | /ɹiˈɹaɪt/ | herschrijven |
| calculator zelfstandig naamwoord | /kæl.kjə.leɪ.tɚ/ | rekenmachine, zakrekenmachine |
| confuse werkwoord | /kənˈfjuːz/ | verwarren, in de war brengen |
| notebook zelfstandig naamwoord | /ˈnoʊtˌbʊk/ | schrift, cahier |
| digit zelfstandig naamwoord | /ˈdɪd͡ʒɪt/ | cijfer |
Phrasal verbs die je zult horen
| Woord | Betekenis |
|---|---|
| come across werkwoord | overkomen |
| find out werkwoord | ontdekken, onderzoeken |
Zinnen om te herhalen
Korte, volledige zinnen uit de video die je in alledaagse gesprekken kunt gebruiken:
- Do you know what a natural number is?
- If a number is not natural, what would you say it is?
- That's what you call integers.
- That's the next thing I'm going to do.
- Let's get rid of this.
Grammatica in deze video
De structuren die de spreker het meest gebruikt, met de exacte woorden uit de video:
| Structuur | In de video |
|---|---|
| Lijdende vorm be + voltooid deelwoord — het gaat om wat er gebeurt, niet om wie het doet | is called · can be written |
| Present perfect have/has + voltooid deelwoord — iets uit het verleden dat nu nog telt | you've seen · you've known · we've talked |
Uitspraak om op te letten
De spreker gebruikt 19 samentrekkingen en verkorte vormen, zoals don't, I'm, you've. Spreek ze kort uit, zoals je ze hoort.
- De klanken “sh” en “zh”: fraction /ˈfɹæk.ʃən/, rational /ˈɹæʃ(ə)nəl/, irrational /ɪˈɹæʃ.(ə.)nəl/
- Lange woorden — let op de klemtoon: imaginary /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/, irrational /ɪˈɹæʃ.(ə.)nəl/, approximate /əˈpɹɑk.sə.mət/, infinity /ɪnˈfɪnɪti/, calculator /kæl.kjə.leɪ.tɚ/
Klanken die Nederlandstaligen lastig vinden:
- Stemhebbende eindmedeklinker — /b/, /d/, /g/, /z/, /v/ niet verscherpen: cube /kjub/, confuse /kənˈfjuːz/, behave /bɪˈheɪv/, subscribe /səbˈskɹaɪb/, resolve /ɹɪˈzɑlv/
- /æ/ — opener dan de Nederlandse “e”: imaginary /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/, fraction /ˈfɹæk.ʃən/, rational /ˈɹæʃ(ə)nəl/, irrational /ɪˈɹæʃ.(ə.)nəl/, calculator /kæl.kjə.leɪ.tɚ/
- /w/ — met ronde lippen: whoa /woʊ/, twist /twɪst/
Zo oefen je met deze video
- Luister de hele video één keer zonder te spreken en noteer de woorden die je niet kent.
- Spreek zin voor zin na op normale snelheid en herhaal elke zin tot je ritme gelijk is aan dat van de spreker.
- Neem jezelf op en vergelijk met het origineel; let daarbij op woorden als imaginary, fraction, rational.
Wat is de Shadowing-techniek?
Shadowing is een wetenschappelijk onderbouwde taalleermethode die oorspronkelijk is ontwikkeld voor professionele tolkentraining en gepopulariseerd door polyglot Dr. Alexander Arguelles. De methode is eenvoudig maar krachtig: je luistert naar native Engelse audio en herhaalt het onmiddellijk hardop — als een schaduw die de spreker volgt met slechts 1–2 seconden vertraging. In tegenstelling tot passief luisteren of grammaticadrills, dwingt shadowing je hersenen en mondspieren om echte spraakpatronen tegelijkertijd te verwerken en te reproduceren. Onderzoek toont aan dat het de uitspraaknauwkeurigheid, intonatie, ritme, verbonden spraak, luisterbegrip en spreekvaardigheid aanzienlijk verbetert — waardoor het een van de meest effectieve methoden is voor IELTS Speaking-voorbereiding en echte Engelse communicatie.