Pratica di Shadowing: WHAT ARE NATURAL NUMBERS? - Impara a parlare inglese con i video
Creazione lezione...
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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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Obiettivi di parlato per questo video
Questo clip aiuta a raggiungere una tappa chiave nella fluency: la capacità di spiegare concetti astratti (come i numeri) in modo chiaro e ordinato. Attraverso il discorso del presentatore, che combina esempi con definizioni, gli apprendenti esercitano la strutturazione logica di un discorso, un milestone fondamentale per comunicare idee complesse in inglese.
Banca di frasi riutilizzabili
- "If a number is natural, it means you can find it in nature" (Per spiegare definizioni)
- "Let's say they are whole numbers plus all negative" (Per semplificare concetti complessi)
- "Don't stop. If it's a natural number, it keeps on going forever and ever" (Per enfatizzare una caratteristica)
- "Okay, what are integers? Well, integers are all these things you've seen" (Per passare a un nuovo argomento)
Migliora le tue aree deboli
Il video è perfetto per esercitare il shadowing in inglese (o "shadow speech"), una tecnica che aiuta a migliorare la pronuncia inglese e la fluidità. Il presentatore usa un tono calmo e un ritmo moderato, ideale per imitare: ascolta una frase, pausa e ripeterla immediatamente, cercando di corrispondere all'intonazione e alla velocità. Attenzione alle pause tra le parole: frasi come "Well, let's find out" hanno una pausa dopo "Well" che dà naturalità. Inoltre, espressioni come "Okay?" o "I love this!" sono utili per mantenere l'attenzione, e il shadowing le rende più automatiche. Pratica quotidianamente con questo clip: il shadow speak non è solo ripetere, ma internalizzare il flusso del discorso inglese. In pochi giorni, noterai che le frasi ti escono più spontaneamente!
La grammatica di questo video
Le strutture che chi parla usa di più, con le parole esatte del video:
| Struttura | Nel video |
|---|---|
| Forma passiva be + participio passato — conta ciò che accade, non chi lo fa | is called · can be written |
| Present perfect have/has + participio passato — un’azione passata che conta ancora adesso | you've seen · you've known · we've talked |
| Consigli con “should” should + verbo — dire che cosa è meglio fare | should know |
| Superlativi the -est / the most … — il massimo o il minimo di un gruppo | the largest · the most popular |
Cos'è la tecnica dello Shadowing?
Shadowing è una tecnica di apprendimento delle lingue supportata da studi scientifici, originariamente sviluppata per la formazione dei traduttori professionisti e resa popolare dal poliglotta Dr. Alexander Arguelles. Il metodo è semplice ma potente: ascolti un audio in inglese di madrelingua e lo ripeti immediatamente ad alta voce — come un'ombra che segue il parlante con un ritardo di solo 1–2 secondi. A differenza dell'ascolto passivo o degli esercizi di grammatica, lo shadowing costringe il tuo cervello e i muscoli della bocca a elaborare e riprodurre simultaneamente i modelli di discorso reale. La ricerca dimostra che migliora significativamente la precisione della pronuncia, l'intonazione, il ritmo, il discorso connesso, la comprensione dell'ascolto e la fluidità del parlato — rendendolo uno dei metodi più efficaci per la preparazione alla prova di speaking dell'IELTS e per la comunicazione reale in inglese.