this post was submitted on 23 Oct 2025
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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
How would anyone get into one of those free, uncountable rooms if they can't see them.
Ever opened a door with the light off?
Yes, since I have hands to feel the door. Hands which, incidentally, are able to help me count things they touch :)
Okay, automatic doors with perfectly precise sensors based on shifts in gravity.
A single portal into all the different rooms might work if you are ok with your continuous room-choosing mechanism having a probability of zero to get you into your chosen room. Not a problem as long as you take everying with you since the probability of hitting some empty room is of course still one.
What about upon entering a room a new normal door is then constructed, allowing re-entry?