So that is really useful theorem if a set is not fine, and then the Union A and Naturals have the same cardinality as a.

And the proof is not.

Difficult.

It would be good if you understand it.

Um?

It is not find it means there exists.

Infinite collection of elements A1.

A2.

A3.

From a right.

So all elements.

So let's say this is B.

We must all right.

Properly it is subset of it.

I think it's clear.

No.

No.

Clearly.

He

SBTRKT be.

Is in a one to one correspondence.

Or with a SBTRKT be that is.

Absolutely clear.

Alright.

And after all, this is clear.

After this is clear.

Be.

Union.

Nature Rose

is in a one to one correspondence.

With beer.

Why?

Becausw they want to one correspondence can be.

Construct it.

Explicitly.

We have

be union and have the same the following shape.

Air one.

Coma one.

82

Komoto

23.

Coma three and so on.

And B CAS Elements A1.

82

A3.

A four one to one correspondence looks like this.

One to one correspondence look like. It looks like this.

And now.

From this tool.

Statements.

Hey.

Minus B.

Union.

See Union end.

Rich equals a union man.

I think it is clear.

Is in a one to one correspondence with a - B.

The union dear.

Which equals C.

Alright, I stop recording.

And.