 if the system \(\Re\) of all real numbers divides into two classes \(\fA_1\), \(\fA_2\) such that every number \(a_1\) of the class \(\fA_1\) is less than every number \(a_2\) of the class \(\fA_2\), then there exists one and only one number by which this separation is produced. (1872: section 5 [1999: 776])