Orchid XP v8 wrote:
> Mike Raiford wrote:
> 

I found Invisible's summary to be a bit confusing, and also seemed to 
have a semi-important error, so here's another quick summary:

The Aleph numbers are "cardinals" which means they represent the size of 
sets.  Aleph_0 is the first infinite cardinal, which is equal to the 
size of the set of natural numbers.  Aleph_1 is the next size that a set 
can have which is larger than Aleph_0.  Beth_1 is the size of the set of 
all real numbers, and it can be proven that the size of this set is a 
"larger infinity" than the size of the set of all natural numbers (so 
Beth_1 > Aleph_0).  It cannot be proven by standard set theory whether 
or not Beth_1 = Aleph_1.  Put another way, it is impossible to prove 
whether or not there are sets which have a size between that of the 
natural numbers and that of the real numbers.

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