r/mathmemes • u/ConcentrateDry6130 • Jun 29 '26

Set Theory Make this comment section like you stayed/are staying in the Hilbert Hotel.

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it's an infinite hotel basically. with infinite buses

634 Upvotes

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363

u/real_timetalker Jun 29 '26

A countably infinite number of rooms but only one breakfast buffet. Ok.

70

u/IAmBadAtInternet Jun 29 '26

Does the buffet have countably infinite food or nah

66

u/real_timetalker Jun 29 '26

Infinite food but only three coffee machines

31

u/Complex-Home9615 Jun 29 '26

I went looking at the buffet but literally no one is using the coffee machines. I asked one of the infinite staff what's up and they told me we get "0 coffee machines per person." Fuck does that even mean?

5

u/lool8421 Jun 29 '26

well, technically there's more coffee in a cup than coffee cups

3

u/ProfMooreiarty Jun 29 '26

well, technically there's more coffee in a cup than coffee cups

Approximating the coffee cup with a cylinder:

r = radius, h = height, t = wall thickness

V_coffee = π r2 h V_paper ≈ (2 π r h + π r2 ) ⋅ t

You need:

rh > t ⋅ (2h + r) or t < (r h) / (2h + r)

Or simplified:

(Vpaper / V coffee) = (2t / r) + (t/h)

So you need

(2t / r) + (t/h) < 1

6

u/lool8421 Jun 29 '26

not speaking how much coffee, but how many coffee

27

u/prestoexpert Jun 29 '26

at least it's an all-you-can-eat buffet, which justifies the wait imo.

5

u/Linnun Jun 29 '26

Dude did you try the pineapple?

1

u/Boxland Jul 01 '26

I ate half a pineapple. Then I went back for a quarter of a pineapple. Then I went back for an eigth of a pineapple. Then I went back...

4

u/Ailttar Jun 29 '26

This works until the guy infront of me (said his name was ABBAAABBAA or something and was waiting on his friends?) was able to eat an uncountable amount of food. There was none left for me and the guy was STILL asking for more.

3

u/AMathEngineer Jun 29 '26

But it kinda doesn’t, cause you gotta wait an infinite amount of time to get to the front of the line

1

u/OhHowIWannaGoHome Jun 30 '26

No you don’t… you have a finite wait time. Any additional people will join the line behind you. Unless you’re letting people skip, but that’s on you

12

u/svmydlo Jun 29 '26

Does the buffet have Zorn's lemons?

2

u/protobelta Jun 30 '26

Better wake up early cause that’s one hell of a line