I in this class, I want you to look at finite and infinite set.
Set can be classified as finite or what?
Infinite set.
Okay.
So set can be
classified as either.
Finance.
Or.
If finance.
Set.
Okay.
What is a final set?
A final set is a set that contains a specific number of elements.
Okay, So final set.
Contains a specific.
Number.
Of elements.
Which means it contains finance or a limited number of elements that is limited.
Norm.
For example, you want to look at the set of weekdays.
That is a set of week.
This.
You are looking at, what, Monday, Tuesday, Wednesday, Thursday and Friday, as you can see.
There is no addition.
There is no reduction.
They are specific.
They are what?
Limited?
There are five in number.
You can't change it.
That is an example of what finite set.
And if finite set.
Is a set that has unlimited number of what element that is unlimited.
Number of elements.
Okay.
What is the meaning of this?
It means it cannot be counted or listed in its entirety.
That is, you cannot.
Cannot.
Cannot count them.
And cannot.
What?
List them in their entirety.
What are the examples of this?
For instance, we are talking about all natural numbers.
You can finish all natural number, can't list all of them or irrational numbers or rational numbers.
All integers.
You cannot count all these numbers.
These are what?
Infinite set.
For instance, if I want to represent natural numbers, I will start by saying one, two, three, four,
five.
Then three dots.
Many are countable.
Okay.
Without an end.
But what you need to know about Infinite Set is there are different levels of finite set.
We are talking about the size not of finite set are the same size.
Okay.
For instance, if you look at.
Natural numbers.
Then you look at real numbers.
They are not of the same size.
I want to ask you which one is bigger?
Ah, which one is smaller?
This.
It's smaller than this, because if you want to look at all natural numbers, you agree with me, you're
going to start from one, two, three and infinite.
But real numbers, real numbers, zero is there minus one?
Is there minus two?
Is there?
Okay.
0.1 is here.
0.04 is here.
These are real numbers.
The square root of two.
Square root of three.
Both irrational and rational.
Proper fraction in proper fraction.
All these are part of what?
Real numbers.
So this is more than this.
So not all infinite sets have what?
The same size.
Okay.
Now let's look at these examples.
The set of all the continents are the.
Finite or infinite.
You know, they are limited.
So they are finite.
Okay.
So you can see.
North America, South America, Europe, Asia, Africa, Australia, Antarctica.
They are limited.
Okay, so they are finite set.
Look at this.
The set of all the US states that start with the letter M are the finite or infinite.
You agree with me?
They are finite.
What about the set of all natural numbers?
We just talked about that now they are worth in finance.
You list them like this.
I see three dots.
They are what?
Infinite set.
What about the set of all real numbers?
We have also seen that what they are worth infinite.
These are to represent the from negative infinity to positive infinity.
Okay, look at this.
The set of all evil prime numbers.
Evil prime.
We only have one evil prime number, and that is two.
It means what it is worth.
It is what finance are seeing this place they are what finance set is the set of all natural number,
finite or infinite.
You agree with me?
They are what infinite is the set?
One, two, three, four.
Finite or infinite?
They are what?
Finite and infinite Set Be empty.
The answer is no.
And if an asset cannot be empty because it contains an unlimited number of elements are all final set
the same size.
We have seen that.
No, they are not of the same size.