On 7/6/2010 10:01 PM, Kevin Wampler wrote:
> 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.

Ok, that makes sense to me now. Yeah, I think my original post was a bit 
mistaken ... I realized pretty quickly after Andrew's posting what it 
meant, but I don't quite think I had the right words to express what I 
was thinking.


-- 
~Mike

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