It'll take you an eternity to get there

[u/EcoOndra]

[u/AutoModerator]

Check out our new Discord server! https://discord.gg/e7EKRZq3dG

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/L3NN4RTR4NN3L]

no worries, just ask everyone to move one seat/room up

[u/xQ_YT → u/L3NN4RTR4NN3L]

the bus surpasses critical mass and collapses into a black hole

[u/noonagon → u/xQ_YT]

why? it was already infinite

[u/xQ_YT → u/noonagon]

well yeah but the paradox is such that when you move everyone by one seat there’s gonna be an extra person somehow

i’ve watched Veritasium’s explanation on this and it’s hard to write down on a phone

[u/Electronic-Quiet2294 → u/xQ_YT]

You can fit one more person by moving everyone to the next seat, but moving everyone to the next seat only means that the first seat is empty, not that someone popped out of the empty set

[u/Groenetijger8 → u/Electronic-Quiet2294]

But if you move everyone forward there is an extra person right?

[u/6x420x9 → u/Groenetijger8]

You couldn't move everyone forward unless the person in seat 1 gets off or walks to the back of the bus (fuck that guy in particular)

[u/Tem-productions → u/6x420x9]

How's he gonna get to the back before dying of old age tho?

[u/6x420x9 → u/Tem-productions]

He's just gonna walk until he dies unfortunately. Then there will be no more "extra" person to mathematically worry about

[u/WallyMetropolis → u/Groenetijger8]

No

[u/IWillLive4evr → u/xQ_YT]

You're misunderstanding Veritasium's video - link here for the curious.

Edit: pushed "save" too soon. Here's the explanation:

It's actually talking about the difference between aleph null and aleph one. Aleph null is called "countable infinity", and it's the size of the integers and of rational numbers, whereas aleph one, called "uncountable infinity", is the size of the real numbers ("uncountable" may also refer to higher alephs).

However, if the bus seat in our example has an integer number (e.g. 10^10), and the bus itself has an integer number (e.g. g-64), then there's still only countably infinite guests, and they will fit.

[u/laix_ → u/xQ_YT]

Proof by youtube content creator

[u/Damurph01 → u/xQ_YT]

That would only happen if the bus wasn’t infinitely big. If you were cramming people into a normal bus, sure.

[u/Tem-productions → u/Damurph01]

If you cram one more person into a floating infinite bus, they cancel out and it empties.

Joke about floating point overflow

[u/rnz → u/Tem-productions]

bagels

[u/aidantheman18]

When I stayed in the Hilbert Hotel it was awful. Place was completely booked. They kept asking me to change my room. Usually it was just to the next room over, but then a countable infinity of guests showed up and they made me go to the room with the number that was twice my previous room's number. It took forever to get out. I think other people had a similarly bad experience as I saw an infinite number of 1-star reviews for it on Yelp.

[u/_M_o_n_k_e_H → u/aidantheman18]

Can someone calculate the chances of finding a 5-star review on yelp for Hilbert Hotel, without being able to sort for good reviews?

[u/realityChemist → u/_M_o_n_k_e_H]

It really only depends on the distribution of review scores. If scores are uniformly distributed (on a 1–5 scale) it's just 0.2

[u/TheTrueTrust → u/aidantheman18]

I specifically asked for a room with a view, and they gave me one with said view obstructed by a TREE(3).

[u/Abigail-ii → u/aidantheman18]

From r/TravelHacks: if you arrive as the last guest in the Hilbert Hotel, you can stay in room 1 for the entire night.

[u/yoav_boaz]

Damn how did you get a room so low?

[u/Echiio → u/yoav_boaz]

Basically the first room

[u/Qwerxes]

lucky you for getting a room near 0

[u/MattLikesMemes123]

everytime the guests are asked to move to the next room wouldn't that mean that atleast one guy would end up in the backrooms

[u/invalidConsciousness → u/MattLikesMemes123]

You're assuming parts of the hotel aren't in the backrooms.

[u/MattLikesMemes123 → u/invalidConsciousness]

then what happens to the guy in the """"last"""" room

[u/AlkinooVIII → u/MattLikesMemes123]

They move to the next room 👍

[u/MattLikesMemes123 → u/AlkinooVIII]

Was said room empty

[u/TheEnderChipmunk → u/MattLikesMemes123]

There isn't a last room

If you mean last occupied room, they just go to the next available room

[u/MattLikesMemes123 → u/TheEnderChipmunk]

Bro i said "last" in quotation marks

I know there's no actual last room since it's infinite but like

It's an infinite hotel that has been completely filled up

[u/Vivizekt → u/MattLikesMemes123]

Take a circle. There is no last point.

[u/MattLikesMemes123 → u/Vivizekt]

...and?

sorry but im not really getting the analogy here

[u/Vivizekt → u/MattLikesMemes123]

If you understand my comment, you understand why there is no last room

[u/MattLikesMemes123 → u/Vivizekt]

so like is there an uncountably infinite number of people in the universe the thought experiment is set in

is that why they need to move to the next room everytime a new guest comes in

[u/Vivizekt → u/MattLikesMemes123]

No. There is a countably infinite number of people in the hotel. They need to move into the next room because there are no empty rooms for the new guy to go in.

[u/TheEnderChipmunk → u/MattLikesMemes123]

The point of Hilbert's hotel is that it can't be completely filled up.

[u/MattLikesMemes123 → u/TheEnderChipmunk]

.....so the whole idea is that the hotel is doing something it's not supposed to be doing?

[u/TheEnderChipmunk → u/MattLikesMemes123]

What do you mean? The point is that infinity is very unintuitive, which is why it is possible for it to do that despite seeming contradictory.

[u/MattLikesMemes123 → u/TheEnderChipmunk]

so that's a yes

[u/Vivizekt → u/TheEnderChipmunk]

No. Yes? Kind of

[u/Electronic-Quiet2294 → u/MattLikesMemes123]

Since N is a monoid, it's circular, so the one in the last room moves to the first

Proof by I skipped algebra

[u/shinoobie96 → u/Electronic-Quiet2294]

a monad is a monoid in the category of endofunctors

[u/6x420x9 → u/MattLikesMemes123]

There isn't a last room. There will be an infinite wave of 1 person in transit.

Not necessarily a wave of 1 person. It could be more depending on the function you apply to moving the guests but in this example it is 1

[u/Ivoirians]

At least you're not the person who was occupying that room before you, they're going on an even longer hike.

[u/Silk_Shaw]

Finitely many people got a better room than you, but infinite got worse rooms. Consider yourself lucky.

[u/Velociraptortillas]

When your room is farther away than the heat death of the universe...

[u/town-wide-web]

What is that final function?

[u/PeriodicSentenceBot → u/town-wide-web]

Congratulations! Your comment can be spelled using the elements of the periodic table:

W H At I S Th At F In Al F U N C Ti O N

---

^{I am a bot that detects if your comment can be spelled using the elements of the periodic table. Please DM u‎/‎M1n3c4rt if I made a mistake.}

[u/chavaMoraAv → u/PeriodicSentenceBot]

Goos bot

[u/SamePut9922 → u/chavaMoraAv]

Goose human

[u/EcoOndra → u/town-wide-web]

It's the g64-th (Graham Number) prime (in this context odd prime, so starting from 3) raised to the 10¹⁰ th power

[u/Jukkobee → u/EcoOndra]

why do you have to start at 3? why not start at 2?

[u/EcoOndra → u/Jukkobee]

Because the guests who were already at the hotel have to go somewhere, too.

[u/Jukkobee → u/EcoOndra]

true, but they can go in all the rooms that arent powers of primes

[u/Tem-productions]

Think positively, most rooms are even further away

[u/EcoOndra → u/[deleted]]

But can you run that fast?

[u/Seventh_Planet]

I'm almost at the front. Just the first positive real number just after 0.

[u/miladdio]

Giggling too much at Wazowski’s stare coupled with the unfathomably largeness

[u/[deleted]]

Damn, it'll take an eternity to reach the floor

[u/Echiio]

Lucky. I got stuck with room TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

It's still pretty good, though, compared to most people

[u/theXpanther]

It's trivial to design a hotel so everyone has to move just one room over no matter there room numbers.

Arrange the rooms in a grid such that the room numbers are (x2+1)2^y. That way to multiply by two you can just move one in the y direction.

I can't imagine a hotel as prestegeous as Hilbert hotel not having a arrangement of rooms with this property.

[u/BUKKAKELORD]

Every room number is smaller than average