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

148 INTRODUCTION TO MATHEMATICS
for the meaning of f, y is either 0 or 1 according as the value of x is integral or otherwise.
Thus f(l) =0, f(2) =, f(2) = 1, f() = 1, and
so on. This choice for the meaning of f(x)
gives a perfectly good function of the argument x according to the general definition of
a function.
A function, which after all is only a sort
of correlation between two variables, is represented like other correlations by a graph,
that is in effect by the methods of coordinate
geometry. For example, fig. 2 in Chapter II
is the graph of the function 1 where v is the
v
argument and p the value of the function.
In this case the graph is only drawn for positive values of v, which are the only values
possessing any meaning for the physical application considered in that chapter. Again
in fig. 14 of Chapter IX the whole length of
the line AB, unlimited in both directions, is
the graph of the function x + 1, where x is the
argument and y is the value of the function;
and in the same figure the unlimited line
AiB is the graph of the function 1-x, and
the line LOL' is the graph of the function x,
x being the argument and y the value of the
function.
These functions, which are expressed by
simple algebraic formulae, are adapted for
representation by graphs. But for some