Georg Cantor Quotes
The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.
Cantor, Georg. "Mitteilungen zur Lehre vom Transfiniten." Zeitschrift für Philosophie und philosophische Kritik, vol. 91, 1887. Printed in Georg Cantor Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, edited by Ernst Zermelo, Julius Springer, 1932, p. 380.
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician. He created set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact he was well aware of.
