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

GENERALIZATIONS OF NUMBERS 81
accordance with this habit the addition of
operations is denoted by + as well as the
addition of numbers. Accordingly we can
write
(+3)+(+1)= +4;
where the middle + on the left-hand side
denotes the addition of the operations +3
and +1. But, furthermore, we need not be
so very pedantic in our symbolism, except in
the rare instances when we are directly tracing
meanings; thus we always drop the first +
of a line and the brackets, and never write
two + signs running. So the above equation
becomes
3+1 =4,
which we interpret as simple numerical addition, or as the more elaborate addition of
operations which is fully expressed in the
previous way of writing the equation, or
lastly as expressing the result of applying
the operation +1 to the number 3 and obtaining the number 4. Any interpretation
which is possible is always correct. But the
only interpretation which is always possible,
under certain conditions, is that of operations.
The other interpretations often give nonsensical results.
This leads us at once to a question, which
must have been rising insistently in the