Re: infinity
- From: Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx>
- Date: Thu, 8 Sep 2005 11:00:49 -0400
David Kastrup said:
> stevendaryl3016@xxxxxxxxx (Daryl McCullough) writes:
>
> > But aleph_0 is not a natural number, so it is incorrect to replace
> > n by aleph_0. However, it is true that the size of the set
> >
> > { 1, 2, ... aleph_0 }
> >
> > is aleph_0.
>
> I think that this is an abuse of notation since it implies a sequence
> ending in aleph_0. But aleph_0 is a singular disconnected value in
> that set. It has no predecessor.
>
> So I'd rather write it as
>
> { aleph_0, 0, 1, 2, ... }
>
> Yes, this set has size aleph_0.
>
>
Well, you only say that because you believe {0,1,2,3...} has size aleph_0 and
that aleph_0+1=aleph_0. However, the way Daryl wrote it makes some sense.
Unfortunately, it seems he meant it the way you prefer, which doesn't solve
anything. When you have an infinite set with infinite members, the vast
majority of the members are infinite. You can't throw ina token infinite
number and expect that to solve anything.
--
Smiles,
Tony
.
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