Well, he should consider himself lucky, since he’s still in one of the early rooms. In fact, almost as good as the first one, since the amount of rooms with numbers smaller than 2×TREE(3) as a percentage of all the rooms, is zero. Almost every other guest has it worse.
I don’t get it. Is “tree” some kind of notation?
TREE is an extremely fast-growing function in set theory. TREE(1) equals 1, TREE(2) equals 3, and TREE(3) equals a number so large that its lower bound easily dwarfs Graham’s Number.
its lower bound easily dwarfs Graham’s Number.
Yo you don’t gotta throw shade on Grahams number like that, it’s doing its best
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Yes, TREE(3) is larger than a googolplex or even graham’s number.
That article is not comprehensible to most people
I am one of them. I still can’t get past the Hotel paradox. To me an infinite number of guests cancels out an infinite number of rooms.
Infinite guests = infinite rooms Infinity + n = infinity To say the bus of unbound guests could just move into infinite rooms seems to give a property of rooms without limit that is not shared with the original infinite guests.
The original premize states the hotel is full. Because the only thing that matches infinite rooms are infinite guests.
Apparently I am very stupid. My sister was right all along.
https://www.youtube.com/watch?v=3P6DWAwwViU
Here is a Numberphile video that describes how large a number we are talking.
Why do I always feel like I need a PhD to understand even the first paragraph of Wikipedia articles about math. Is that just me?
yeah where’s the Simple English Wikipedia article for Graham’s number
Go get your PhD and write one yourself!
What about our friend TREE(Graham’s Number)
Numberphile did a video on TREE(g64) so you gotta go bigger.
BB(TREE(3)) :)
TREE(Rayo(10100))
TREE(yomomma)
Needs more recursion
Also is your username from stormlight archive?Also is your username from stormlight archive?
:)
Haven’t seen them in a while. Hope they’re doing well
man hes gone have to do a lot of walking again… Offtopic: The funny thing is TREE(3) is an absurdly long distance, independent of the physical unit. Even TREE(3) times the planck length is unimaginable long, as the ratio between a meter and the planck length is absolutely neglectable against such super large numbers.
It’s so large that the number of digits it has is too large to represent, and the number of digits in that number is too large to represent, and so on for a number of times that is also far too large to represent.
Let’s say you have to move to the infinite room. How can someone check out of the hotel?
There is no infinity room, but there is an infinity pool
You can check out any time you like
The only issue is that if I have to travel to an infinite distance to the lobby, I’ll never check out.
Don’t worry, you can never be put in a room with an infinite number, only an arbitrarily large one. That’s the idea of the hotel; it has an infinite number of rooms, but every room has a finite number, since you can count forever without reaching infinity.
Whew, I was worried as the infinite passanger on that bus that I’d be put into an infinite room.
Just put a sign on the door telling everyone who comes there to go to the inverse wing. Or go set up in the inverse wing of the hotel yourself.
Everyone in the place is moving right along the infinite axis… But there’s a whole empty wing of the hotel if you go left at the front desk.
That’s my secret, I’m always moving.
