 The basic idea of this equivalence is owed to Hume (whence the current name of the principle); and it had of course been exploited to great effect by Cantor, well before Frege wrote the  Grundlagen.[15]  Without the use of one-one correspondences in this way, Cantor would not have been able to motivate his later groundbreaking idea that there are distinct infinite numbers (see Cantor 1891). 