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

VARIABLES 17
The first point to notice is the possibilities
contained in the meaning of some, as here
used. Since x +2 =2+x for any number x,
it is true for some number x. Thus, as here
used, some does not exclude any. Again, in
the second example, there is, in fact, only one
number x, such that x +2=3, namely, only
the number 1. Thus the some may be one
number only. But in the third example,
any number x which is greater than 1 gives
x +2 > 3. Hence there are an infinite number of numbers which answer to the some
number in this case. Thus some may be
anything between any and one only, including both these limiting cases.
It is natural to supersede the statements
(2) and (3) by the questions:
(2') For what number x is x+2 =3;
(3') For what numbers x is x+2 > 3.
Considering (2'), x+2 =3 is an equation, and
it is easy to see that its solution is = 3 -2 = 1.
When we have asked the question implied in
the statement of the equation x +2 =3, x is
called the unknown. The object of the solution of the equation is the determination of
the unknown. Equations are of great importance in mathematics, and it seems as
though (2') exemplified a much more thorough-going and fundamental idea than the
original statement (2). This, however, is a
complete mistake. The idea of the undeter