Pratique du Shadowing: WHAT ARE NATURAL NUMBERS? - Apprendre l'anglais à l'oral avec la vidéo
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166 phrases
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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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Vocabulaire et conseils d’expression pour cette leçon
Cette leçon d’expression orale de niveau B1 s’appuie sur la vidéo « WHAT ARE NATURAL NUMBERS? ». Les mots qui reviennent le plus souvent : negative, root, square, natural, imaginary. Cette vidéo contient 166 phrases et 1559 mots à répéter en shadowing. La partie parlée dure 12:03. Le locuteur parle à un rythme régulier d’environ 129 mots par minute, confortable pour le shadowing. 88 % des mots font partie des 3 000 mots les plus courants en anglais, le vocabulaire est donc facile à suivre.
Vocabulaire clé de cette vidéo
Les 15 mots les plus avancés de la vidéo, avec leur prononciation et leur sens :
| Mot | Prononciation | Sens |
|---|---|---|
| imaginary adjectif | /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/ | imaginaire |
| fraction nom | /ˈfɹæk.ʃən/ | fraction |
| rational adjectif | /ˈɹæʃ(ə)nəl/ | rationnel, rationnelle |
| decimal nom | /ˈdɛs.ɪ.məl/ | décimal, système décimal |
| integer nom | /ˈɪn.tɪ.d͡ʒə(ɹ)/ | entier, nombre entier |
| irrational adjectif | /ɪˈɹæʃ.(ə.)nəl/ | irrationnel |
| multiply verbe | /ˈmʌltɪplaɪ/ | multiplier |
| approximate adjectif | /əˈpɹɑk.sə.mət/ | approximant |
| infinity nom | /ɪnˈfɪnɪti/ | infinité |
| cube nom | /kjub/ | cube |
| rewrite verbe | /ɹiˈɹaɪt/ | réécrire, récrire |
| calculator nom | /kæl.kjə.leɪ.tɚ/ | calculatrice, calculette |
| confuse verbe | /kənˈfjuːz/ | rendre perplexe, confondre |
| notebook nom | /ˈnoʊtˌbʊk/ | cahier, calepin |
| digit nom | /ˈdɪd͡ʒɪt/ | chiffre |
Les verbes à particule que vous entendrez
| Mot | Sens |
|---|---|
| come across verbe | avoir l'air de |
| find out verbe | découvrir, savoir |
| put up verbe | placer |
Des phrases à répéter
Des phrases courtes et complètes de la vidéo, à réutiliser dans la conversation de tous les jours :
- 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.
La grammaire de cette vidéo
Les structures que le locuteur utilise le plus, avec les mots exacts de la vidéo :
| Structure | Dans la vidéo |
|---|---|
| Voix passive be + participe passé — l’accent est mis sur ce qui arrive, pas sur qui le fait | is called · can be written |
| Present perfect have/has + participe passé — une action passée qui compte encore maintenant | you've seen · you've known · we've talked |
Prononciation à surveiller
Le locuteur utilise 19 contractions et formes réduites, comme don't, I'm, you've. Prononcez-les sous leur forme courte, telles que vous les entendez.
- Les sons « sh » et « zh »: fraction /ˈfɹæk.ʃən/, rational /ˈɹæʃ(ə)nəl/, irrational /ɪˈɹæʃ.(ə.)nəl/
- Mots longs — placez bien l’accent: imaginary /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/, irrational /ɪˈɹæʃ.(ə.)nəl/, approximate /əˈpɹɑk.sə.mət/, infinity /ɪnˈfɪnɪti/, calculator /kæl.kjə.leɪ.tɚ/
Les sons difficiles pour les francophones :
- /tʃ/ et /dʒ/ — à ne pas adoucir en « ch » et « j »: imaginary /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/, integer /ˈɪn.tɪ.d͡ʒə(ɹ)/, digit /ˈdɪd͡ʒɪt/, supernatural /ˌsu.pəɹˈnæ.tʃə.ɹəl/
- /r/ anglais — langue recourbée, sans frotter la gorge: imaginary /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/, fraction /ˈfɹæk.ʃən/, rational /ˈɹæʃ(ə)nəl/, integer /ˈɪn.tɪ.d͡ʒə(ɹ)/, irrational /ɪˈɹæʃ.(ə.)nəl/
Comment s’entraîner avec cette vidéo
- Écoutez la vidéo en entier une fois sans parler et notez les mots que vous ne connaissez pas.
- Répétez phrase par phrase à vitesse normale, en reprenant chacune jusqu’à ce que votre rythme corresponde à celui du locuteur.
- Enregistrez-vous et comparez avec l’original, en faisant attention à des mots comme imaginary, fraction, rational.
Qu'est-ce que la technique du Shadowing ?
Le Shadowing est une technique d'apprentissage des langues fondée sur la science, développée à l'origine pour la formation des interprètes professionnels. Le principe est simple mais puissant : vous écoutez de l'anglais natif et le répétez immédiatement à voix haute — comme une ombre suivant le locuteur avec un décalage de 1 à 2 secondes. Les recherches montrent une amélioration significative de la précision de la prononciation, de l'intonation, du rythme, des liaisons, de la compréhension orale et de la fluidité.