ABSTRACT
The difference of signs belongs, traditionally, only to numbers and magnitudes, and is intimately associated with addition. It may be allowed that the notation cannot be usefully employed where there is no addition, and even that, where distinction of sign is possible, addition in some sense is in general also possible. But we shall find that the difference of sign has no very intimate connection with addition and subtraction. To make this clear, we must, in the first place, clearly realize that numbers and magnitudes which have no sign are radically different from such as are positive. Confusion on this point is quite fatal to any just theory of signs.
