쉐도잉 연습: WHAT ARE NATURAL NUMBERS? - 영상으로 영어 말하기 배우기

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Hello, welcome back to another video.

I would like you to know today what the properties of numbers are.

Okay?

I know we all use numbers every day, but do you know what real numbers are?

Do you know what a natural number is?

If a number is not natural, what would you say it is?

Unnatural or supernatural?

Well, let's find out.

so properties of numbers i'm just going to

start with what i just asked natural numbers

if a number is natural it means you can find it in nature

and when humans try to count or try to talk about numbers They do this a lot.

One, two, three.

See the first number?

That's the first natural number.

One.

Not zero.

There's no zero among natural numbers.

So the set of natural numbers are the numbers you can count on your fingers.

One, two, three, four, five.

All numbers are positive.

So if you want to know natural numbers, you just need to look at your fingers.

Whatever you find is a natural number.

Okay, so set of natural numbers will be positive one, positive two, like that, three, four, all the way to the end.

Don't stop.

If it's a natural number, it keeps on going forever and ever.

Okay, let's go to number two.

So if a number is not a natural number, what is it?

It must be on the other side of the negative.

Okay, so, but before you cross to the other side of the negative, there's a number just before positive 1.

That number is called 0.

0 is not a natural number, but it belongs to the set of numbers called whole numbers.

So, our next definition is the set of whole numbers.

If a number is a whole number, well it is either a natural number or it's a zero.

Zero plus the set of natural numbers.

I love this!

numbers

so it's a whole numbers are just natural numbers including zero

that's it that's all we got to say let's move on to the next set let's talk about integers

why am I writing like this?

Come on.

Integers.

Okay, what are integers?

Well, integers are all these things you've seen.

Whole numbers plus whole negative.

I don't want to say negative whole numbers, but if that's how you're going to understand it,

Oh, let's say they are whole numbers plus all negative.

Oh, there's no negative natural number.

Just know if we change these signs to negative, just look at your number line.

Okay?

You walk into a classroom, you see the number line from negative infinity to zero to positive infinity.

That's what you call integers.

Put that in your head.

I'm just going to write the number line from left to right.

no fractions no decimals we don't call them whole numbers

but they are whole numbers

but still have negative portion of the whole that's confusing just

stick to it just look at the number line all the numbers you see are what you call integers keep

that in your head or in your notebook

and then later in your head let's move on the next thing let's go to real numbers whoa

so real numbers are real okay

if a number is a real number it means it is any of these things

that you've known or maybe fractions decimals rational or irrational numbers just know

that every number you know is a real number unless there's a part of it

that is not real

and the part of a number is not real you say it is an imaginary number

or a complex number i'm going to explain what an imaginary number is

or what a complex number is but just know

that every number you know is real all numbers fractions decimals

whole numbers negative positive zeros infinity All those numbers are real, okay?

Real numbers.

All numbers that are not imaginary.

Okay?

So, if a number is not imaginary, it's a real number.

This is the largest group of numbers you'll be dealing with, okay?

So if a number is not real, it's going to be imaginary.

Now what's an imaginary number?

That's the next thing I'm going to do.

Let's get rid of this.

I know this is in your head already.

Let's go.

Come on.

So, what's an imaginary number?

Imaginary number.

Let me give you a simple example.

The square root of 4 is positive 2.

Because positive 2 times positive 2 is going to give you 4.

So the root of 4 is going to be 2.

Now let's look at, what if I said that the square root of 4 is negative 2?

Will I be correct?

Yes, I will be because negative 2 times negative 2 is still going to be positive 4.

So, what if I say the square root of negative 4?

And that becomes impossible because it cannot be negative 2 and it cannot be positive 2

because both of these are answers to square root of 4.

So what's the square root of negative 4?

Yeah, it's a bit twisted.

What if we rewrite this as the square root of negative 1 multiplied by 4?

Negative 1 multiplied by 4 gives you the square root of negative 1 multiplied by the square root of 4.

Ah, now we can come back to getting our answer positive to or negative to whatever we choose,

100

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.

116

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

166

and don't stop learning god bless you bye Thank you.

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이 비디오를 통해 자연수, 정수 등 수학 용어의 영어 표현을 익히고, 영어로 개념을 설명하는 능력을 기르며, IELTS 스피킹에서 요구되는 명확한 논리적 설명 스킬을 연습할 수 있습니다. 또한 일상적인 대화에서의 자연스러운 발화 패턴을 체험하여 영어 발음 교정에도 도움이 됩니다.

들어야 할 소리: 연결된 발음

영어의 연결 발음을 주의 깊게 듣습니다. 예를 들어 "what are"은 /wɑːtər/로 연결되고, "you can"은 /juːkæn/로 줄어듭니다. "natural numbers"에서 "natural"과 "numbers" 사이에는 약간의 연음이 있어 /ˈnætʃrəl ˈnʌmbərz/가 아닌 /ˈnætʃrəlˈnʌmbərz/처럼 들릴 수 있습니다. 이러한 연결 발음을 파악하면 shadow speak 연습 시 더 자연스러운 발음을 구사할 수 있습니다.

원어민처럼 말하기: 리듬과 강세

원어민의 리듬을 따라하기 위해서는 강세가 중요합니다. "natural numbers"에서 "natural"은 첫 번째 음절에 강세를 두고 /ˈnætʃrəl/로 발음하고, "numbers"는 /ˈnʌmbərz/처럼 첫 번째 음절에 강세를 줍니다. 또한 "Well, let's find out."에서 "Well"은 약간의 강세를 주어 자연스러운 대화의 흐름을 이어갑니다. shadowspeaks 연습 시 이러한 강세와 리듬을 반복해서 따라하면, 영어 발화의 자연스러움이 크게 향상될 것입니다. 특히 IELTS 스피킹에서는 명확한 강세와 리듬이 점수에 큰 영향을 미치므로, 이 비디오의 발화 패턴을 철저히 분석하고 모방하는 것이 좋습니다.

핵심 용어 정리

자연수(natural numbers): 1, 2, 3...과 같이 자연에서 세는 수로, 0을 포함하지 않습니다.
정수(integers): 양의 정수, 0, 음의 정수를 모두 포함하는 수 집합입니다.
연결 발음(connected speech): 영어에서 단어 사이가 자연스럽게 연결되는 현상으로, shadow speech 연습의 핵심 요소입니다.

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문형	영상 속 표현
수동태 be + 과거분사 — 누가 하는지보다 무슨 일이 일어나는지에 초점	is called · can be written
현재완료 have/has + 과거분사 — 과거의 일이 지금도 관련이 있을 때	you've seen · you've known · we've talked

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쉐도잉(Shadowing)은 원래 전문 통역사 훈련을 위해 개발된 언어 학습 기법으로, 다언어 학자인 Dr. Alexander Arguelles에 의해 대중화된 방법입니다. 핵심 원리는 간단하지만 매우 강력합니다: 원어민의 영어를 들으면서 1~2초의 짧은 지연으로 즉시 소리 내어 따라 말하는 것——마치 '그림자(shadow)'처럼 화자를 따라가는 것입니다. 문법 공부나 수동적인 청취와 달리, 쉐도잉은 뇌와 입 근육이 동시에 실시간으로 영어를 처리하고 재현하도록 훈련합니다. 연구에 따르면 이 방법은 발음 정확도, 억양, 리듬, 연음, 청취력, 말하기 유창성을 크게 향상시킵니다. IELTS 스피킹 준비와 자연스러운 영어 소통을 원하는 분들에게 특히 효과적입니다.

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쉐도잉 연습: WHAT ARE NATURAL NUMBERS? - 영상으로 영어 말하기 배우기

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이 비디오로 배울 수 있는 것

들어야 할 소리: 연결된 발음

원어민처럼 말하기: 리듬과 강세

핵심 용어 정리

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쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법