Mengenlehre

Fishburn and Hughes: "German for 'set theory': a mathematical term designating the theory of G. Cantor (1829-1920) on the relationship between finite numbers and infinitude. Cantor examines the comparisons of infinite collections, starting from the observation of the equivalences in a series such as 1,2,3,4 which could equally express, or be expressed by, 2,4,6,8, so that 1 could be represented by 2, 2 by 4, 3 by 6 and so on. Thus any integer can represent all its multiples and all its multiples can be elevated to multiple power, so that 1 may be 6036 and also 6036 squared, and so on. Furthermore 1 can undergo equal fragmentation. The point ultimately arrived at is that any one cardinal number may be symbolic of any other, and of all others and, by extension, of infinitude; moreover there are a host of potentially infinite numbers. This theory led Cantor to the paradoxical conclusion that the universe is composed of an infinitude of points, as is a yard of the universe, or a fraction of that yard, making the most infinitesimal point on earth symbolic of the macrocosm. Borges discuses this theory in Etern. 77-9. In the Mengenlehre, the aleph denotes a higher power than that of finite numbers. It also talks of a plurality of alephs." (128)