d8

Number Title

What It Is...

1

Tattoo Arrow Niner

When trying to represent the biggest rational number, one must develop shorthanded systems. You can see some of them here: https://en.wikipedia.org/wiki/Large_numbers
One continues to invent new notations to represent higher ordered calculations. (10↑↑↑10, 10→10→10…, etc.) The arrowscalculations representing other arrowcalculations get increasingly more complex, and take up increasingly more chalkboard room. Eventually you get to the point where you must use surface area on your skin to symbolize the arrows. This is the number written in the arrows encompassing the entirety of one’s skin, using 9’s (because 10’s are less timeefficient to write).

2

Mump’s Number

Nobody actually knows what this number is or what it represents, but it is apparently very very big.

3

Supertask Infinite Beta

An endotemporal being in a lower dimension begins counting upwards from 1 to infinity. We observe this as having been done in a finite amount of time. This is the number they achieve.

4

Flanck’s Number

The theoretical combinatorial analysis of all possible spatial configurations for everything in the universe.

5

Supertask Inverse Gamma

A god halts the person halfway to their destination. Because of this they cannot move. Inverse of the minimum distance they are uninhibited from taking.

6

Naughty Noght

The sum of all naughty numbers (2, 3, 18, 21, 47, 69, 3857, etc…)

7

Divergence Denominator

The number of possible universes, pending universes split at the most minute circumstances.

8

The Argentum Value

The value of a particular person, given in picograms of molten silver, by the Androsphinx of Argentum.

The Near Hotel
CountTroll Country: It is wellknown that Trolls are obsessed with counting. Bridgetrolls in particular, as the vast amounts of time between meals offer ample opportunity to count up hairs on their hands, or stones in a river, or flies in the air.
They hate it when they’re discovered counting, and frequently use their discovery as an excuse to eat a person. (Often, they’ll introduce a ‘riddle’ to offer the victim a chance. These will often be such things they’ve determined, such as “how many leaves are in this forest?”)
In the Infinity Hotel, a troll can start counting and never stop. It might start walking down the corridor and never return. Trolls encountered this way, moving from room to room, counting as they go, will often be extraordinarily famished and ready for a meal.
They’re found, sometimes, in the later sections of the Near Hotel, still trudging on, counting and eating as they go. Sometimes they’re found even further in. Sometimes they change. Those travelled furthest are the most dangerous: they have likely eaten dozens of people on their counting pilgrimage. Nothing compares to the ones that are coming back. But no troll could have possibly gotten to Infinity and back right? Right?!...
When encountered, they are likely to give you a riddle, usually related to some room number nearby. They’ll ask you to factor it, or ask in some convoluted way to divide it by 4. Fail, and they will eat you. Succeed, and they will probably still try to eat you.
Troll Speed without rest: 4mph
Average distance between rooms: 15ft
Troll Speed in terms of rooms: 1,408 rooms/hour
33,792 rooms/day
12,334,080 rooms/year
CountTroll Country is around room 15 million. Here trolls start to reconsider their pilgrimages, and many stop to live out the rest of their days waylaying visitors and eating hotel mice. They don’t usually know how to use the Mystic Elevator. Heaven help us if they did.
The Last Restroom: This is the last bathroom before there are no more bathrooms… for the entire Hotel (theoretically, there should be an infinite number of restrooms, but nobody’s found any after this one). As it needs to alleviate some niinfinite peoples, one can imagine it is quite busy.
To accommodate this, The Last Restroom was built on the Complex Plane, and as such it contains both components real and imaginary. This makes it incredibly efficient and useful at times, and impeccably infuriating at others. Hence the duality: 1) You can only imagine where the pee goes! 2) Nobody wants to deal with a mathematically “Complex” toilet.
The Far Hotel
Encrypted Algorithmic Rooms: One creates a variabledependant algorithm which generates a constantlyshifting room number far into the hotel. Both the equation and the variable become factors in where the room will to be. These types of rooms are typically used for secret dealings.
Variables include:
How does the concierge greet you?
What number does the Goblin Prince wear on his crown today?
How many 9’s and how many arrows will the Human Calculator write between 5:17pm and 5:20pm?
What is the emotional state of the Atomic Bear?
Word Room Numbers: If you treat the alphabet as a base 26 number system, you can create room numbers by writing out words and sentences. A = 1; B = 2 ; … ; Y = 25 (equivalent for base 26 system) ; Z = 0. These rooms tend to be quite far apart, as a difference in letters early in the sentence will equate to unconscionable distances. All of these numbers remain rational, however, and so they belong in the Far Hotel. Describing places by mnemonic sentences can be more useful than their numbers within certain ranges.
These rooms are frequented by Paromancers, who establish alcoves in effort to uncover the secrets of the Hotel and language.
Sentence Room Examples:
“Faraday”
6,1,18,1,4,1,25
“Derivatives Are Hardly Just That”
4,5,18,9,22,1,20,9,22,5,19,1,18,5,8,1,18,4,12,25,10,21,19,20,20,8,1,20
“The Wailing Bell of the Endless Hotel
Carries Far Indeed,
Though Strong as It May, As Loudly It Bay
None Will Hear It Plead”
20,8,5,23,1,9,12,9,14,7,2,5,12,12,15,6,20,8,5,5,14,4,12,5,19,19,8,15,20,5,12,3,1,18,18,9,5,19,6,1,18,9,14,4,5,5,4,20,8,15,21,7,8,19,20,18,15,14,7,1,19,9,20,13,1,25,1,19,12,15,21,4,12,25,9,20,2,1,25,14,15,14,5,23,9,12,12,8,5,1,18,9,20,16,12,5,1,4
Source: Charles Gilchrist 
The Deep Hotel
The Mail Room: There may be an infinite space in the hotel, but somebody still needs to deliver the mail. Nobody is sure where the Mail Room came from, who runs it, or how it delivers the mail to every conceivable place within the hotel, but it does. Infinity finds a way.
It is a marvel of automation and magic  letters and packages sort themselves, flying through the air like swooping owls, or rolling along the ground like stomping automaton. A series of chutes, conveyor belts, fans, pulleys, levers, and tornados whisk the mail away to wherever it may.
It all makes use of the Mystic Elevator, with entire compartments stuffed to the seams with oblong packages and crisp letters to be whisked to whoknowswhere. Many have surmised that the Mail Room is part of the organism of the Hotel, much like the Elevator itself.
More mystifying, however, are the addresses on the letters and packages. They are written in a number system completely alien to human understandings of mathematics. More so than that, they aren’t even written in a system used by other rooms of the Deep Hotel, giving rise to the belief that there are several incomprehensible alien systems of mathematics, some more convenient or alien than others.
The addresses are as strange and varied as can be: some hurt to look at, some smell strange, or must be licked to understand the address, or are very clearly modified demonic summoning circles. Does YogSothoth run the Mail Room? The strange man in the Lobby says: “yes!”. Given the room’s size, it’s not impossible, like everything in the Hotel.
The Great Fold: Space gets strange in the Deep Hotel. Things stop being a neat linear algebra somewhere along the line and start being a very messy linear algebra. The Hotel still progresses in a line, mind you, but it is a line that folds and warps, that bends back upon itself and does several 360 spins before pirouetting to mad applause. In The Great Fold, this linearity is pushed to the limit.
To say this is confusing to newcomers is an understatement. They soon find that marching forward isn’t quite so, well… forward. They find that rooms don’t follow any logic they can understand, leaping plots of distance, speed, and time in ways that make them rather inaccessible.
Things found here are strange and inhospitable: they move about the hallway like video game glitches, darting in and out of higher dimensions without care to frivolous lower beings. They are facsimiles of being. Don’t touch them.
Home of the Gelatinous Tesseract. Or, at least, its main entry point into our reality. Its presence attracts multitudes of teleportation aficionados.