1984, with Dick Tahta*Images of Infinity*.

Answer quickly, without thinking too long about it: what proportion of
(base 10) numbers, up to 1000, and up to 10 million, contain at least one
digit '9'? Many people answer "about a tenth", but that's much
too small. More than a quarter of the numbers up to 1000 contain at least
one '9', as do more than *half* the numbers up to 10 million. *Images
of Infinity* contains a wonderful, simple, proof that *most*
numbers, when written in base 10, contain at least one digit '9' in them.
Consider the first 9* ^{n}* numbers written in base 9, none
of which contains a '9'. Now consider the first 10

This little book contains many such gems about infinity: fractal curves; limits of strange series; "proofs" that pi equals 2, or 4; the Hilbert Hotel with its large number of rooms; a Jorge Luis Borges story about an infinite book; and more. I'm not sure who the target audience is intended to be: some of the stuff is pretty basic, some is very deep, yet there is no bibliography of further reading for the curious. But it is an interesting confection.