Loosely speaking, the real numbers are all numbers that can be represented as fractions (rational numbers), whether proper or improper—and all numbers in between the rational numbers. That is, the real numbers comprise the rational numbers and all limits of Cauchy sequences of rational numbers, where the Cauchy sequence is with respect to the absolute value metric. (More formally, the real numbers are the completion of the set of rational numbers in the topology induced by the absolute value function.) The real numbers contain all integers, all fractions, and all irrational (and transcendental) numbers, such as π, e, and 2^½. There are uncountably many real numbers between 0 and 1; in contrast, there are only countably many rational numbers between 0 and 1.