Cantor continued to correspond with Dedekind, sharing his ideas and seeking Dedekind 's opinions, and he wrote to Dedekind in 1877 proving that there was a 1-1 correspondence of points on the interval [0, 1] and points in p-dimensional space. Cantor was surprised at his own discovery and wrote:
Kantor patuloy na lumiham sa Dedekind, pagbabahagi ng kanyang mga ideya at mga naghahanap Dedekind 's opinions, at siya wrote sa Dedekind sa 1877 proving na may 1-1 correspondence ng mga puntos sa pagitan ng [0, 1] at puntos sa p-dimensional space . Kantor ay ulat sa kanyang sariling pagkatuklas at wrote: