Alright.
So interval 01 has the same cardinality.
Is the set of all subsets of Naturals.
So binary representation of a number.
From zero 01.
Their first
The 1st digit is 0. After that there can be only zeros and ones.
Well, you must understand what it means, so decimal representation is so by the way, what it means it means.
This is for crafts.
We have
1/4.
When this is.
One is.
And this is.
1.
32 and so on.
So this is.
Zero and the value is like this.
So binary representation of real numbers. So as soon as you understand this.
Now they want to one correspondence with.
Subsets of Naturals is like that.
So this number.
Is.
In Correspondence.
Or with.
Subset.
2.
3.
5.
67899
11
And so on.
You understand how I constructed this subset.
I simply wrote down the number of the place, number of year one appears, or one appears. Is the 2nd on the 2nd place on the third place?
On the 5th.
678 ninth, 11th, 12th and so on.
So if you have an arbitrary subset of Naturals.
You can construct the corresponding.
Real number from 01.
And.
Well, in the opposite direction for any real number you can construct the.
Subset of integers.
So this is the idea of the proof, I hope it is understandable.
But it is not the end of the proof.
Becausw
but the number.
011
and zeros.
Is the same as.
1.
011111.
If you add together Sirius, you will see these two numbers coincide.
But these two numbers have in correspondence different subsets of Naturals.
So this is a little difficult here.
But
one can overcome it easily, by the way.
OK, I stop recording.
Go to do it.