Hotel Infinity (2013)

(to the tune of Hotel California)

On a dark desert highway
Route 17 was the name
Problems in mathematics
Definitions to blame
Stretching into the distance
There's a shimmering light
A full room for all of N
But could I sleep for the night?
Cantor stood in the doorway
I knew his theorems well
I was thinking to myself,
What successes aleph null?
Move from n to n plus one
I heard on the PA
As they opened up their doors
I thought I heard them say

Welcome to the Hotel Infinity
Not a lonely place
Such a lonely place
Plenty of room at the Hotel Infinity
Any time of year
You can find room here

I was starting to miss the
Cantor Schroeder Bernstein
When a group of yellow, yellow pigs,
All walked in.
A bus came to the courtyard, infinite twice,
Some sort to do the math, and some sort to be nice.

So I called up the Kelly,
"Please bring me my swine",
He said, "If you dona't have one here yourself, I got two-eighty-nine."
And still those piglets are calling from far away,
Move you down to room 2n,
And again the next day!

Welcome to the Hotel Infinity
Not a lonely place
Such a lonely place
Fillin' it up at the Hotel Infinity
Room for everyone
And we're never done...

Now in pigs are streaming,
All real numbers to fit,
Cantor said, "We are all just yellow pigs here
In a countable set"
And in Kelly's chambers,
They gather seventeen,
They cut the pork chops with their knives,
Only once ever seen.

Last thing I remember,
I was looking for a proof,
I had to find a way to show,
This could not be the truth.
"Relax," said the math man,
We write programs to receive,
You can prove it any time you like,
But you will not believe!