Kevin Wald: Banned From Aleph

(With uncountably many apologies to Leslie Fish.)

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As we approached the Aleph Inn and tried to park our car,
They noticed there was one of us for every point in R;
Their room-list had the wrong transfinite cardinality,
Alas -- for it was Aleph Null and our bunch was C.

   So we're banned from Aleph, almost all,
   Banned from Aleph -- their hotel's just a little small.
   We may be only aleph-one (or -twelve or -fifty-four)
   But Aleph has no room for any more.

The desk clerk tried to fit us in, but each prospective list
He gave us, we diagonalized to show him who he'd missed.
He grew a bit irate, for we were starting to be pests --
We each were chatting up a different subset of his guests.

   And we're . . .

He said we could omega-tuple up (this plan assumes
That aleph-zero sleep in each of aleph-zero rooms).
The manager came over, though, and said in somber voice
That such a scheme would violate the Axiom of Choice.

   And we're . . .

We phoned another Aleph Inn, it didn't help a bit;
The clerk at Aleph One could prove he couldn't prove we'd fit.
At last, I called the local shul when services were done;
The cantor let us spend the night in Temple Beth-Sub-One.

   'Cause we're banned from Aleph, almost all,
   Banned from Aleph -- their hotel's just a little small.
   We may be only aleph-one (or -twelve or -fifty-four)
   But Aleph has no room for any more.