[neutralino]

Originally Posted by Profpat As I recall Georg Cantor proved that there are three infinities. Aleph 0 The infinity of numbers. ( "bigger' if you will ) Aleph 1 The infinity of points. ( "biggest" and last ) Aleph 2 The infinity of curves.

There are infact, infinitely many infinities. But, these infinities are not the same; they were invented to describe cardinality of sets. Aleph-0 (pronounced aleph-null) is given to a set that is countably infinite. A countably infinite set is a set from which a bijection can be made with the natural numbers (i.e. one can construct a map that is one-to-one onto between the set and the natural numbers).

Aleph-1 is the defined as a larger "infinity"; the cardinality of the real numbers is aleph-1. You can then extend the idea up to aleph-n where n is an ordinal number (some weird number in set theory invented to deal with these infinities).