74

86

the whole, since corresponding to every number N there is a distinct
and separate even number, its double. So likewise
the multitude of powers of ten, or numbers written by a single
figure 1, followed by zeros 1, 10, 100, 1000, 10000, etc.
is just as great as that of all whole numbers.

The multitude of rational fractional values is
denumeral, since any one may be reached in
one way of writing them one by one. Namely, we
begin with writing
0/1 1/0
which are not properly rational fractional values,
and now we proceed by the following rule.
Having gone through the row, go through the whole row again, and insert between each
successive pair of fractions a fraction having for
its numerator and denominator respectively the
of the numerators and the sum of the denominators of the two fractions

86

the whole, since corresponding to every number N there is a distinct
and separate even number, its double. So likewise
the multitude of powers of ten, or numbers written by a single
figure 1, followed by zeros 1, 10, 100, 1000, 10000, etc.
is just as great as that of all whole numbers.

The multitude of rational fractional values is
denumeral, since any one may be reached in
one way of writing them one by one. Namely, we
begin with writing
0/1 1/0
which are not properly rational fractional values,
and now we proceed by the following rule.
Having gone through the row, go through the whole row again, and insert between each
successive pair of fractions a fraction having for
its numerator and denominator respectively the
of the numerators and the sum of the denominators of the two fractions