Symbols are part of the language of mathematics. The use of symbols gives mathematics the power of generality: The ability to focus not only on a specific object, but also on a collection of objects. For instance, variables— symbols with the ability to vary in value used in place of numbers—make it possible to write general equations. Consider the equation 3 + 4 = 7. This equation is specific. Suppose we are interested in all pairs of numbers whose sum is equal to 7. Using variables, x and y, to denote the two numbers, we would write the general equation x + y = 7. The variables, x and y, stand for many different pairs of numbers; x can be 5 and y can be 2 or x can be 9 and y can be -2. The only condition is that the sum of x and y is 7.

Symbols also include special notation for mathematical operations, like + for addition...