…the realm where infinity dwells,
Hilbert's Hotel, with infinite cells.
rooms stretch on, without a border.
In this abode where numbers play,
The infinite guests find a stay.
Each room is filled, yet there's always space,
A puzzle that time cannot erase.
"Welcome," says Hilbert, with a smile so sly,
"To my hotel, where limits defy.
For though each room is occupied,
There's always room for one more inside."
A new guest arrives, weary from the road,
Hilbert says, "Fear not, we'll find you abode.
Move each guest to the next in line,
Room n to n+1, and all will be fine."
And so the guests shuffle, one by one,
In this infinite dance that's never done.
The halls echo with footsteps, a never-ending beat,
paradox and reality meet.
What of a bus, with infinite crowd?
"Bring them in!" Hilbert laughs aloud.
"Just move each guest to twice their room's number,
The odd ones will fit, without any encumber."
So the infinite guests find their place,
lost in time and space.
Hilbert's Hotel, with its doors always open,
A monument to the infinite
In this place, where numbers roam free,
The impossible becomes reality.
A shelter for infinity, under its spell,
Welcome to the enigma of Hilbert's Hotel.
