he then proved convergent by showing them to be monotonically increasing and bounded above. His study of the convergence of series includes a test equivalent to Raabe's test, which he discovered independently and at about the same time as Raabe. Other important ideas in the work include a general definition of a function and a definition of an equality between two plane figures if they can both be divided into a finite equal number of pairwise congruent pieces. He first dissuaded his son from the study of non-Euclidean geometry, but by 1832 he became enthusiastic enough to persuade his son to publish his path-breaking thoughts. János's ideas were published an appendix to the Tentamen. Notes References A. Todea, F. Maria, M. Avram, Oameni de știință mureșeni - Dicționar biobibliografic, CJ Mureș Biblioteca Județeană Mureș, tipografia Mediaprint SRL, 2004 External links Further references on Farkas Bolyai The Bolyai Memorial Museum 1775 births 1856 deaths 18th-century Hungarian mathematicians 19th-century Hungarian mathematicians People from Sibiu County Hungarian Calvinist and Reformed Christians Hungarian inventors Members of the Hungarian Academy of Sciences