# Review of The Cat in Numberland, by Ivar Ekeland

The Cat in Numberland

by Ivar Ekeland

illustrated by John O’Brien

Cricket Books, Chicago, 2006.  60 pages.

I love this book!  It takes the concept of “countability” which I learned about in upper division math classes and graduate school, and makes those concepts accessible and understandable for elementary school children!

It starts with a hotel in Numberland, run by Mr. and Mrs. Hilbert.  The Numbers all live in this hotel, the Hotel Infinity.  Number One lives in Room 1.  Number Two lives in Room 2, and so on.  “For instance, Number One Million Two Hundred Thirty-Four Thousand Five Hundred Sixty-Six lives in Room 1,234,566.”

The numbers have certain games they like to play together, and there are certain quirks to the owners.

Some more fun begins when Zero comes to visit and wants to stay, but the hotel is full.  How could they possibly fit him in?

They come up with an ingenious solution:

“Everyone moves up one room:

Number One moves to Room 2,

Number Two moves to Room 3,

Number One Million Two Hundred Thirty-Four Thousand Five Hundred Sixty-Six moves to Room 1,234,567, where he finds a bigger bed and is more comfortable.

Room 1 is now empty, and Zero moves in and goes to sleep.

All the other Numbers go back to sleep in their new rooms, and Mr. and Mrs. Hilbert go back to sleep in their old room.

Only the cat by the fireplace does not go back to sleep, because she is trying to figure it out.

The hotel was full, she thinks.  There was one guest in each room.  Now it is full again, and there is still one guest in each room, but there is one more guest in the hotel!  Zero was outside.  Now he has moved in, and yet nothing has changed!  How is that possible?”

This is only the beginning of the perplexities facing the cat at this amazing hotel, based on the work of great mathematicians Georg Cantor and David Hilbert.

I find this book absolutely delightful!  I wish it had been around when I was taking Real Analysis.  Or, better yet, when my little boy was obsessed with infinity, and kept inventing “numbers” that were “bigger than infinity.”  I think he would have enjoyed this story.