On this occasion only three of our original set are left, namely, 1, 4, 9. Such processes of correlation may be varied endlessly.
The most interesting case of the above kind is the case where our one-one relation has a converse domain which is part, but not the whole, of the domain. If, instead of confining the domain to the first ten integers, we had considered the whole of the inductive numbers, the above instances would have illustrated this case. We may place the numbers concerned in two rows, putting the correlate directly under the number whose correlate it is. Thus when the correlator is the relation of
to
, we have the two rows:
When the correlator is the relation of a number to its double, we have the two rows:
When the correlator is the relation of a number to its square, the rows are: