What is the Hilbert Inn Paradox?

Suddenly I wanted to see a few paradoxes that I had learned before,

I always think these mathematicians are so cute.

Make some paradoxes difficult for yourself,

Before and after is not the same,

Let yourself be left behind.

But it may be these are the same difficulties,

A spark that inspires them.

I just wrote that there are parts that can be equated with the whole,

So I couldn't sleep.

In the spirit of rigorous science,

and more than ten years of arithmetic occupational diseases,

I have to talk about what is the Hilbert Hotel Paradox?

Legend has it that there is a magical inn,

Of course, this hotel was assumed by mathematicians.

There is no such thing as our finite world.

Interjection digression:

Something that doesn't exist,

Sure enough, you can study it unscrupulously.

It is said that this hotel has countless rooms,

And it's all full.

Suddenly, another guest came to stay,

The normal boss will definitely say that he can't live,

Fully booked.

But the owner of this magical hotel said,

No problem, can stay.

So he made a mysterious operation:

Since the hotel has an infinite number of rooms,

So he placed the original guests in room 1 in room 2.

The original guests of room 2 are placed in room 3,

And so on,

This freed up room 1 for new guests.

What's even more amazing is that

The boss eats an operation,

Discover that it can accommodate unlimited guests.

Because this process is constantly repeated,

He was able to keep a steady stream of guests in the hotel.

Wow,

Earn the sky!