there is a difference in the use of the two sets of variables. We study the general properties of the relationship between x and y while a , b , and c have unchanged values. We do not determine what the values of a , b , and c are; but whatever they are, they remain fixed while we study the relation between the variables x and y for the whole group of possible values of x and y . But when we have obtained the properties of this correlation, we note that, because a , b , and c have not in fact been determined, we have proved properties which must belong to any such relation. Thus, by now varying a , b , and c , we arrive at the idea that a x + b y − c = 0 represents a variable linear correlation between x and y . In comparison with x and y , the three variables a , b , and c are called constants. Variables used in this
way are sometimes also called parameters.
Now, mathematicians habitually save the trouble of explaining which of their variables are to be treated as "constants," and which as variables, considered as correlated in their equations, by using letters at the end of the alphabet for the "variable" variables, and letters at the beginning of the alphabet for
the "constant" variables, or parameters. The two systems meet naturally about the middle of the alphabet. Sometimes a word or two of explanation is necessary; but as a matter of fact custom and common sense are usually sufficient, and surprisingly little confusion is caused by a procedure which seems so lax.
The result of this continual elimination of definite numbers by successive layers of parameters is that the amount of arithmetic performed by mathematicians is extremely small. Many mathematicians dislike all numerical computation and are not particularly expert at it. The territory of arithmetic ends where the two ideas of "variables" and of "algebraic form" commence their sway.