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

68 INTRODUCTION TO MATHEMATICS
equation in the form x2 + (0 Xx) -4 = 0. For,
by the laws stated above, x2+(0Xx)-4=
x2+0-4=x2-4. Hence the equation x2-4
=0, is merely representative of a particular
class of quadratic equations and belongs to
the same general form as does x2- 3x + = 0.
For these three reasons the symbol 0, representing the number zero, is essential to
modern mathematics. It has rendered possible types of investigation which would have
been impossible without it.
The symbolism of mathematics is in truth
the outcome of the general ideas which dominate the science. We have now two such
general ideas before us, that of the variable
and that of algebraic form. The junction of
these concepts has imposed on mathematics
another type of symbolism almost quaint in
its character, but none the less effective. We
have seen that an equation involving two
variables, x and y, represents a particular correlation between the pair of variables. Thus
x +y -1 =0 represents one definite correlation, and 3x +2y-5=0 represents another
definite correlation between the variables x
and y; and both correlations have the form
of what we have called linear correlations.
But now, how can we represent any linear
correlation between the variable numbers x
and y? Here we want to symbolize any
linear correlation; just as x symbolizes any