In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number a/b is a "good" approximation of a real number α if the absolute value of the difference between a/b and α may not decrease if a/b is replaced by another rational number with a smaller denominator.