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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Vocabulario y notas de pronunciación para esta lección
Esta lección de conversación de nivel B1 se basa en el vídeo “WHAT ARE NATURAL NUMBERS?”. Las palabras que más se repiten: negative, root, square, natural, imaginary. Este vídeo tiene 166 frases y 1559 palabras para practicar shadowing. La parte hablada dura 12:03. El hablante mantiene un ritmo constante de unas 129 palabras por minuto, cómodo para el shadowing. El 88 % de las palabras está entre las 3.000 más comunes del inglés, por lo que el vocabulario es fácil de seguir.
Vocabulario clave de este vídeo
Las 15 palabras más avanzadas del vídeo, con su pronunciación y significado:
| Palabra | Pronunciación | Significado |
|---|---|---|
| imaginary adjetivo | /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/ | imaginario |
| fraction sustantivo | /ˈfɹæk.ʃən/ | fracción |
| rational adjetivo | /ˈɹæʃ(ə)nəl/ | racional |
| integer sustantivo | /ˈɪn.tɪ.d͡ʒə(ɹ)/ | entero |
| irrational adjetivo | /ɪˈɹæʃ.(ə.)nəl/ | irracional |
| multiply verbo | /ˈmʌltɪplaɪ/ | multiplicar, amochiguar |
| approximate adjetivo | /əˈpɹɑk.sə.mət/ | aproximado |
| infinity sustantivo | /ɪnˈfɪnɪti/ | infinidad |
| cube sustantivo | /kjub/ | cubo |
| rewrite verbo | /ɹiˈɹaɪt/ | reescribir |
| calculator sustantivo | /kæl.kjə.leɪ.tɚ/ | calculador, calculadora |
| confuse verbo | /kənˈfjuːz/ | confundir, barahustar |
| notebook sustantivo | /ˈnoʊtˌbʊk/ | cuaderno, libreta |
| digit sustantivo | /ˈdɪd͡ʒɪt/ | dígito, cifra |
| whoa | /woʊ/ | so, cho |
Phrasal verbs que vas a escuchar
| Palabra | Significado |
|---|---|
| come across verbo | pasarse a |
| find out verbo | averiguar, anoticiarse |
| put up verbo | colgar |
Frases que vale la pena repetir
Frases cortas y completas del vídeo que puedes reutilizar en la conversación diaria:
- 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.
Gramática en este vídeo
Las estructuras que más usa el hablante, con las palabras exactas del vídeo:
| Estructura | En el vídeo |
|---|---|
| Voz pasiva be + participio pasado — importa lo que ocurre, no quién lo hace | is called · can be written |
| Present perfect have/has + participio pasado — una acción pasada que sigue importando ahora | you've seen · you've known · we've talked |
Pronunciación a tener en cuenta
El hablante usa 19 contracciones y formas reducidas, como don't, I'm, you've. Dilas en su forma corta, tal como las oyes.
- Los sonidos de “sh” y “zh”: fraction /ˈfɹæk.ʃən/, rational /ˈɹæʃ(ə)nəl/, irrational /ɪˈɹæʃ.(ə.)nəl/
- Palabras largas — cuida el acento: imaginary /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/, irrational /ɪˈɹæʃ.(ə.)nəl/, approximate /əˈpɹɑk.sə.mət/, infinity /ɪnˈfɪnɪti/, calculator /kæl.kjə.leɪ.tɚ/
Sonidos difíciles para hispanohablantes:
- /v/ — no es /b/: los dientes tocan el labio inferior: behave /bɪˈheɪv/, resolve /ɹɪˈzɑlv/
- /z/ — sonora, no /s/: confuse /kənˈfjuːz/, resolve /ɹɪˈzɑlv/
- /dʒ/ — no es la “y” ni la “ch”: imaginary /ɪˈmæd͡ʒɪˌn(ɛ)ɹi/, integer /ˈɪn.tɪ.d͡ʒə(ɹ)/, digit /ˈdɪd͡ʒɪt/
Cómo practicar con este vídeo
- Escucha el vídeo entero una vez sin hablar y anota las palabras que no conoces.
- Haz shadowing frase por frase a velocidad normal, repitiendo cada una hasta que tu ritmo coincida con el del hablante.
- Grábate y compara con el original, prestando atención a palabras como imaginary, fraction, rational.
¿Qué es la Técnica de Shadowing?
Shadowing es una técnica de aprendizaje de idiomas respaldada por la ciencia, desarrollada originalmente para la formación de intérpretes profesionales y popularizada por el políglota Dr. Alexander Arguelles. El método es simple pero poderoso: escuchas audio en inglés nativo y lo repites en voz alta de inmediato, como una sombra que sigue al hablante con solo 1-2 segundos de retraso. A diferencia de la escucha pasiva o los ejercicios de gramática, el shadowing obliga a tu cerebro y músculos de la boca a procesar y reproducir simultáneamente patrones de habla reales. Las investigaciones muestran que mejora significativamente la precisión de la pronunciación, la entonación, el ritmo, el habla conectada, la comprensión auditiva y la fluidez al hablar, convirtiéndola en una de las metodologías más efectivas para la preparación del IELTS Speaking y la comunicación en inglés en el mundo real.