Can you completely fill a hotel with infinite rooms?

[Bobby_2021]

?

There are infinite number of rooms in the hotel.

Can every room be occupied?

?

[Phil King]

Interesting video about countable and uncountable infinities. 

[Sir Oberon]

Infinity is only possible if there is a finite number.  Without a finite number, infinity would have nothing to stand on. Or,  something always needs nothing.  Absolute nothing is impossible to imagine, because we are something.  Infinity is the same principle, needing the finite to exist.  Every room can be filled or the finite would collapse inward and become infinitely small filling every room.  Or the rooms could become infinitely large always making more room for the finite.

Get on the bus, and don't stop!

[Bobby_2021]

I have come to the conclusion that it is impossible to fill all the rooms of an infinite hotel. 

[Phil King]

1 hour ago, Bobby_2021 said:

I have come to the conclusion that it is impossible to fill all the rooms of an infinite hotel. 

How do you refute the solution proposed in the video I posted?

[Osaid]

Yeah you just need an infinite amount of guests

[vibv]

2 hours ago, Osaid said:

Yeah you just need an infinite amount of guests

And time to get them in there.

[Bobby_2021]

On 10/8/2023 at 9:14 PM, Phil King said:

How do you refute the solution proposed in the video I posted?

The problem discussed in video is a different question.

I am talking about empty rooms.

The video is talking about if every person from the infinie bus gets a room. I don't refute anything said in the video. I am saying a different problem.

Can you "exhaust" a countable infinity is my question?

Will it be exhausted?

Should it be exhausted?

Like all infinites it spans on forever. So there are always more rooms.

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[Bobby_2021]

With regards to the thing in the video I do have a small problem.

 

If the members have names that extends to infinity, then there should be atleast one member who doesn't not have a room. As explained by the diagonalization problem.

 

Why not build an extra room and house them? Such a room need not be numbered even. Or it could be numbers as 0.1 or -1 or the name of the dude itself. 

[vishnusavestheday]

Another problem with the experiment is that any "infinite" room in the hotel requires a definite volume -- a sleeping area has to take up a definite amount of space. Is there a qualifying factor that defines an infinite guest too? 

 

What if one such guest (ie a talking T-Rex) needs a room and he doesn't fit? In even Googolplex universes, there is room to contain reiterations of the same matter along multiple, alternating timelines.

Any of these qualifications limits infinite objects. You're talking about a hotel larger than a googolplex hotel-- a hotel that could be more than a library of time itself.

[Hojo]

I think the rooms are always full

Edited October 21, 2023 by Hojo

[Thought Art]

@vibv or do you?

[vibv]

9 hours ago, Thought Art said:

@vibv or do you?

Else it would be just an always full hotel. Or how would you empty such a hotel? It's the same problem backwards.