The Corner

Hilbert’s Hotel

My friends at MathematiciansPictures.com have a terrific poster of Hilbert’s Hotel, with an explanation by me (for those who missed it in in my July 2005 Diary on NRO).

Now, if you’ll excuse me, I have to go back to the singing game I was teaching to the kids. OK, kids, where had we got to? Oh, right:

There are aleph-null bottles of beer standing on the wall,

Aleph-null bottles of beer standing on the wall;

And if just one bottle should accidentally fall,

There’ll be aleph-null bottles of beer standing on the wall.

There are aleph-null bottles of beer standing on the wall,

Aleph-null bottles of beer standing on the wall;

And if just one bottle should accidentally fall,

There’ll be aleph-null bottles of beer standing on the wall.

There are aleph-null bottles of beer standing on the wall,

Aleph-null bottles of beer standing on the wall…

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