An Infinite Hotel Can Be Fully Booked, Here's How

To the people claiming that this video copied content from Veritasium or TedEx or some other channel: no. This is a very famous thought experiment, Hilbert's "paradox of the grand hotel", dating back to the 1920s. It is not at all surprising that there is more than one video on youtube about a well known and interesting bit of mathematics.

When ever I hear this solution I imagine how hard it must be for the first person to walk out of the hotel, because their room was changed so many times…

If I was a guest in this hotel, I'd be super annoyed that I'm being asked to change rooms every 15 minutes!

Ted Ed posted this ober 9 years ago Veritasium a year ago

But you are saying that there is going to be always another combination of X and Z which is why it is an infinity the combination you get is just a part of the infinity and its an infinity with infinite number of different combinations with X and Z. So its just a normal infinity with the solution in the begging or move to a room with an odd number. Because with this logic I can say that even with the first bus I can always say that there is going to be a bigger number.

Veritasium's idea but in a different style

Most explanations of this paradox follow the problem of including a finite number of new guests with the problem just one infinitely-long bus with a countably-infinite number of passengers, in which the proprietor of the hotel relocates the existing guests to the room number that's their starting one doubled, leaving all the infinitely many even-numbered rooms occupied and the infinitely many odd-numbered ones available for the passengers, who could, if you'd like, be assigned room 2n-1, n representing their seat number on the bus. Then the explanations go to the infinite amount of that type of bus mentioned earlier. You skipped that problem I explained myself. Also, there are explanations that don't use the table with the zig-zagging line, but utilize prime numbers as proven by Euclid that there was an infinite quantity of during 300 BCE. The existing guests would be reassigned room number 2^n, the passengers on the first bus: room 3^n. Bus 2: room 5^n. This solution houses all existing and all new guests of all those buses alike, though rooms will be left vacant as long as the numbers they're labeled with aren't pure powers of any of the prime numbers.

WHAT? YOU COPYED AN OLD VIDEO? BUT WILL SOME CHANGES?

I'd rather not.

if there was infinite people then he would also have infinite money, he could just quit in 1 day of the job and live his life.

But what’s a strategy for it if there’s an infinite amount of floors on every infinite bus?

🤣 man imagine typing those names into a computer

Man I love this animation style so refreshing 😁

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In physical world there is nothing infinite, it's a mathematical expression when something is very big compared to another thing. We can consider earth size an infinite to human size and sun size the same, and sun is bigger than the earth.

I swear I heard this exact same thing on a different channel years ago

This is like life .... confusing.

This dude never run out of contents. Danm it.

How come it says the names only consist of X and Z but you can clearly see there is a Y