> > Note that there is some dispute in the mathematical world over how big > c is. Some suggest that it is a rather small infinite cardinal, possibly > aleph-one, meaning the second smallest one (just above aleph-zero, > which is the cardinality of the integers). Others suggest that it may > be larger, possibly much larger, bigger than aleph-(aleph-zero). > > Hal > >
My memory is fading somewhat about transfinite cardinal numbers. However, it seems to me that c \leq \aleph_1. \aleph_1 is the cardinality of the set of all sets of cardinalilty \leq\aleph_0. Since c is the cardinality of the set of all subsets of N, which is a subset of the set of all sets of cardinality \leq\aleph_0. What has never been proven is that c=\aleph_1, although it is widely suspected. ---------------------------------------------------------------------------- Dr. Russell Standish Director High Performance Computing Support Unit, University of NSW Phone 9385 6967 Sydney 2052 Fax 9385 7123 Australia [EMAIL PROTECTED] Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks ----------------------------------------------------------------------------
