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

FUNCTIONS 149
functions this representation would be very
misleading without a detailed explanation, or
might even be impossible. Thus, consider
the function mentioned above, which has the
value 1 for all values of its argument x, except
those which are integral, e.g. except for x = 0,
x==l, x=2, etc., when it has the value 0.
Its appearance on a graph would be that of
the straight line ABA' drawn parallel to the
y
A' B C C Cs C4 A
B, 12 j 14 5
X' O 1 2 3 4 5 X
y
Fig. 20.
axis XOX' at a distance from it of 1 unit of
length. But the points Ci, C2, C3, C4, etc.,
corresponding to the values 1, 2, 3, 4, etc., of
the argument x, are to be omitted, and instead of them the points B1, B2, B3, B4, etc.,
on the axis OX, are to be taken. It is easy
to find functions for which the graphical
representation is not only inconvenient but
impossible. Functions which do not lend
themselves to graphs are important in the