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

146 INTRODUCTION TO MATHEMATICS
"arguments" of the functions in which they
appear. Thus t is the argument of the function 20 Xt, and x is the argument of the function x+1. If s=20Xt, and y=x+l, then s
and y are called the "values" of the functions
20 Xt and x + 1 respectively.
Coming now to the general case, we can
define a function in mathematics as a correlation between two variable numbers, called
respectively the argument and the value of
the function, such that whatever value be
assigned to the "argument of the function"
the value of the "value of the function" is
definitely (i.e. uniquely) determined. The
converse is not necessarily true, namely, that
when the value of the function is determined
the argument is also uniquely determined.
Other functions of the argument x are y =2,
y =x2+3x+1, y=x,ylogx, y=sin x. The
last two functions of this group will be
readily recognizable by those who understand
a little algebra and trigonometry. It is not
worth while to delay now for their explanation as they are merely quoted for the sake
of example.
Up to this point, though we have defined
what we mean by a function in general, we
have only mentioned a series of special functions. But mathematics, true to its general
methods of procedure, symbolizes the general
idea of any function. It does this by writing