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@cute@deadinsi.de ok so imagine you have an infinite hotel that has an infinite number n of rooms, the hotel is full. Then another person checks in, says "Hey I'd like a room please.", the guy at the front desk says "No problem, we're full!", so they ask every person in all n rooms to move up one number. The person in room 1 moves to room 2, the person in room 2 moves to room 3, and so on until the person in room n moves to room n+1 - so the new arrival can stay in room 1.

@cute@deadinsi.de Then, all of a sudden, out of nowhere, an infinite bus pulls into the front drives. The bus driver gets out and goes to the front desk and asks "Hey, I have an infinite number n of people on this bus, and none of them booked a hotel beforehand, can they stay here?"

Once again, the guy at the front desk says "No problem, we're full!". Once again, the front desk guy calls up every guest in the hotel, this time saying "Multiply your room number by two and move into that room." The guests grumble a bit, but this shit happens when you're staying in an infinite hotel - the new arrival in room 1 moves to room 2, the person in room 2 moves to room 4, and so on until the person in room n+1 moves to room 2n+2.

The front desk then checks in all infinite people on the bus into the odd numbered rooms in the infinite hotel.

@cute@deadinsi.de The bus driver sits down in the hotel lobby's bar with a beer, surprised his gambit actually paid off.

He turns around in his stool and is shocked to see an infinite number c of infinite buses each carrying an infinite number n of people. What the fuck do they do now?!

The reception guy greats the infinite number of an infinite number of people, with a smile. "Come on in, we're full up!" He's practically overflowing with mathematical joy at this point, as he realizes there are at least 5 different ways he could organize all of these people into his hotel...

@cute@deadinsi.de Choose your own adventure time: which method of organization should the hotel reception guy use?

A. Prime Powers Method
B. Prime Factorization Method
C. Interleaving Method
D. Triangular Number Method
E. Arbitrary Enumeration Method

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Sunbeam City 🌻

Sunbeam City is a Libertarian Socialist solarpunk instance. It is ran democratically by a cooperative of like-minded individuals.