‘Below the waterline of the number iceberg’ introduces numbers other than positive integers. Integers are all whole numbers, positive and negative, and can be arranged along a number line. These can be added, subtracted, and multiplied easily, but when divided they form fractions (decimals are simply fractions with 10 as the denominator). Irrational numbers are numbers that are not equal to any fraction. Within irrationals are algebraic numbers, which solve polynomial equations with integer coefficients. Non-algebraic numbers are known as transcendental numbers. Real numbers comprise all possible decimal expansions.