An introduction to mathematics, by A. N. Whitehead.

SYMBOLISM OF MATHEMATICS 63
subtle idea, and by its existence make it easy
to exhibit the relation of this idea to all the
complex trains of ideas in which it occurs.
For example, take the most modest of all
symbols, namely, 0, which stands for the number zero. The Roman notation for numbers
had no symbol for zero, and probably most
mathematicians of the ancient world would
have been horribly puzzled by the idea of the
number zero. For, after all, it is a very
subtle idea, not at all obvious. A great deal
of discussion on the meaning of the zero of
quantity will be found in philosophic works.
Zero is not, in real truth, more difficult or
subtle in idea than the other cardinal numbers.
What do we mean by 1 or by 2, or by 3?
But we are familiar with the use of these ideas,
though we should most of us be puzzled to
give a clear analysis of the simpler ideas
which go to form them. The point about zero
is that we do not need to use it in the operations of daily life. No one goes out to buy
zero fish. It is in a way the most civilized
of all the cardinals, and its use is only forced
on us by the needs of cultivated modes of
thought. Many important services are rendered by the symbol 0, which stands for the
number zero.
The symbol developed in connection with
the Arabic notation for numbers of which it
is an essential part. For in that notation the