Page:IntroductionToMathematicsWhitehead.pdf/69

Thus the first use of ${\displaystyle 0}$ was to make the Arabic notation possible—no slight service. We can imagine that when it had been introduced for this purpose, practical men, of the sort who dislike fanciful ideas, deprecated the silly habit of identifying it with a number zero. But they were wrong, as such men always are when they desert their proper function of masticating food which others have prepared. For the next service performed by the symbol ${\displaystyle 0}$ essentially depends upon assigning to it the function of representing the number zero.

This second symbolic use is at first sight so absurdly simple that it is difficult to make a beginner realize its importance. Let us start with a simple example. In Chapter II we mentioned the correlation between two variable numbers ${\displaystyle x}$ and ${\displaystyle y}$ represented by the equation ${\displaystyle x+y=1}$. This can be represented in an indefinite number of ways; for example, ${\displaystyle x=1-y}$, ${\displaystyle y=1-x}$, ${\displaystyle 2x+3y-1=x+2y}$, and so on. But the important way of stating it is

Similarly the important way of writing the equation ${\displaystyle x=1}$ is ${\displaystyle x-1=0}$, and of representing the equation ${\displaystyle 3x-2=2x^{2}}$ is ${\displaystyle 2x^{2}-3x+2=0}$. The point is that all the symbols which represent variables, e.g. ${\displaystyle x}$ and ${\displaystyle y}$, and the symbols