Just go to the infinite plus one room. no need for everyone to shift.
Long walk and it’s nowhere near the ice machine.
It’s fine, you just need to prove there is an infinite number of other inhabitants who would want to swap rooms.
Ah there he is hiding. Disguised with diaper and sock.
I like how this gif loops, so it looks like he’s spitting back into the bottle.
This is actually an issue caused by the hotel staff not allocating their rooms efficiently. When the first wave of infinite guests showed up, they should have assigned them to odd numbered rooms. Then theres still an infinite number of vacant even numbered rooms.
Even if several more waves of infinite guests show up, you can assign them to rooms numbered 4n+2, 8n+4, 16n+8…
That way, the hotel will always have rooms left over.
Heresy! The staff should assign the initial wave of guests to EVEN numbered rooms with a dark chocolate on their pillow. Future assignments must be to 4n+1, 8n+3, 16n+5…
Your heretical tyrany of the highest order will be purged. Only the pure must survive.
Nah they should have just assigned them to every prime room
Or you could just walk to room infinity + 1 and not disturb an infinite number of guests, dick.
There was actually a numberphile of this like 2 days ago. https://youtu.be/47qEMTMKRdA
You can also just ask the staff to change the room numbers and send everyone an update. That way you get a room, no one is disturbed and people running the hotel have an infinite amount of work to do!
But it would take an infinite amount of time to get there!
Is it better to inconvenience one person an infinite amount, or an infinite amount of people a medium amount?
I feel like my odds of avoiding getting my ass kicked are better inconveniencing just one person.
I’ll get Zeno to shoot arrows at you to motivate you.
The journey of a thousand miles begins with the first step.
… Well, better get to walking.
Eh, I’ll get there the same time whether I leave now or tomorrow.
We are not talking about a thousand miles but infinite miles. That’s not the same order of magnitude at all but a factor of infinity
Well you’re definitely not going to get there if you spend all day explaining infinity to people.
Don’t worry, I spend a finite amount of time doing it
You can’t actually. If there’s an infinite number of rooms and infinite guests occupying them then there are no open rooms.
Next-best strategy: make the set of guests who have to be moved arbitrarily sparse, so that 0% of the hotel’s guests need to be bothered. Oh dear, that’s still infinity of them.
This is a great plan, but it is critical to not be the person to notify each guest. Infinite calls to inconvenience infinite people sounds like hell.
You mean ~0%. 0 is 0
Depends on the size of the infinities. If you have an infinite natural number of guests, but infinite real number of rooms, then you have more rooms than guests.
If you can see doors to enter each room, then they are countable.
How do you know the uncountable doors aren’t there? You wouldn’t be able to see them amyway
Wrong: ∞±n = ∞
The concept of infinity is well-defined in mathematics. It goes much deeper than that, with countability and differently-sized infinities, but if there are infinite rooms, you always have space.
Yes, but walking down the hallway you’ll never find an open room. Space can be made but you can’t just go to the ∞+1 room.
I understand the idea behind this, but I always felt that it was a flawed concept.
Maybe my understanding of complex math is limited…but I’m gonna keep pretending I’m smarter than everyone while I enjoy life in my delusional kingdom.
Also this reminds me of the question “can god create a boulder so big that he can’t lift it?”
The concept of infinity is to mathematicians as god is to Christians.
Infinity is effectively just bullshit.
I’m found of pointing out to my students that there’s a very practical reason to care about “infinity” in math:
While nothing every reaches “infinity”, things absolutely do reach a point where they violently fly to pieces and catch on fire.
So I teach my students to substitute the phrase “explodes and catches on fire” where they see an equation that “approaches infinity”.
I find it helps them pay attention to a subject that is otherwise bullshit. Infinity itself is bullshit, but it has a place in math: telling us when to quickly duck behind a good solid oak table.
The comparison doesn’t work. Maths are abstract, you don’t “believe” in it. You build a consistent theory with minimum assumptions (axioms) and if something stops being consistent, it means some of your assumptions don’t work and you need to change them to build a better theory. Maths is an abstract tool, not a representation of reality.
Infinity is just a concept you can define. There are tools to demonstrate something is true over an infinite space and obviously, you need those for a lot of basic maths. You’re not going to go anywhere in basic arithmetic or geometry if you can’t prove anything works over the infinite set of numbers or the infinite space.
Furthermore, while mathematicians admit that math is entirely man-made construct, which is also the reason we have irrational constant, christian do no such thing.
Imaginary numbers are a perfect example of that. It’s basically just “Okay, in the common number theory, you can’t get the square root of a negative number. What if you could?”. And what do you know, you can build a consistent theory where square root of -1 exists, and it has surprising properties.
Intuitively, good luck trying to make sense of it. But it doesn’t matter, it works, and it’s useful to build other stuff. That in turn can be used as modelling tools in physics and all.
I think it makes sense intuitively. It’s just most of us aren’t really trained since childhood to work with inaginary numbers. Sure, it’s not a 1:1 mapping to your fingers, but it’s not that unintuitive. Like when I do certain calculations I go into a second dimension of numbers where I can move around just as in the first dimension, because those calculations are outside of our current physical reality.
I say current as if our reality will change somehow somewhen lol.
0/5 stars. We stayed here for an infinite amount of time over the holiday. Every 10 minutes the staff moved us to a different room! We didn’t even get a chance to unpack our infinite luggage.
This isn’t even unexpected. Once a person unwilling to change room is in first position, they stay there and considering that those people exist, this will happen eventually in the Infinite Hotel
But couldn’t you just skip the room if that happens? Eventually somebody will be willing to change rooms.
Until the second room is also occupied by someone like this. And the third and the fourth… It’s just a question of time
Yeah, as long as there’s an infinite number of people willing to move, it’ll work.
Ugh, getting everybody moved will take forever!
Considering this simple case, it will take just the time for the slowest guest to move to the next room as they can all take their luggage and move to the next room that should be vacant by the time they reach it.
However, this is considering a magic comms system that lets all guest know to move a room instantly. In the case this is not available, the speed of light is the limiter and then it takes forever.
Using the case with instantaneous communication, it is possible to take forever by trying to host a countable infinite amount of people as this is usually done by moving the original guests to the room that is double the current one and the new guests to each odd number left. In this situation, the original guests will take forever as for bigger numbers, the guests have to move more and more rooms each time.
Sorry for the rant, I’ve seen too many Hilbert hotel videos
Perhaps the hotel staff bring in a guest each day at a preset time. They just have to all move rooms at 5pm.
Like hell I’m moving.
That’s the infidel hotel across the street
As long as finitely many guests like this specimen stay put you’re okay.
Even if infinitely many guests want to stay put, as long as for every room, there is a later room willing to move, you’re OK.
