In our base-ten system, there is a range of square numbers, 1,4,9,16,25 etc. Of these very many consist of a mixture of odd and even digits. Is this subset countable? There is a much smaller subset, 4, 64, 400, 484, etc, which consists of only even digits. Is this countable? And there is a very special subset which is definitely countable, consisting of the squares with only odd digits - 1 and 9. As far as I can see, there is no relationship between these subsets, except that they add together to the "master"set.

## Countable infinities

In our base-ten system, there is a range of square numbers, 1,4,9,16,25 etc. Of these very many consist of a mixture of odd and even digits. Is this subset countable? There is a much smaller subset, 4, 64, 400, 484, etc, which consists of only even digits. Is this countable? And there is a very special subset which is definitely countable, consisting of the squares with only odd digits - 1 and 9. As far as I can see, there is no relationship between these subsets, except that they add together to the "master"set.