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.
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?