Since what follows the 5 is another copy of the expression for a, we infer that a4=20a so that a3=20 or, ifyou prefer, a is the cube root of 20. We will call on this technique again in Chapter 7 when we introduce so-called continued fractions.
Does the class of fractions provide us with all the numbers we could ever need? As mentioned earlier, the collection of all fractions, together with their negatives, form the set of numbers known as the rationals, that is all numbers that result from whole numbers and the ratios between them. They are adequate for arithmetic in that any sum involving the four basic arithmetic operations of addition, subtraction, multiplication, and division will never take you outside the world of rational numbers. Ifwe are happy with that, this set of numbers is all we require. However,we explain in the next section how numbers such as a above are not rational.
