|
![](/i/fill.gif) |
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.
Post a reply to this message
|
![](/i/fill.gif) |