🚀 go-pugleaf

Greg d. Moore wrote:
> 
> Tosser wrote:
> >
> > Charles R. Rutledge wrote:
> >
> > > Sorry, Guy.  Both the set of all integers and the set of even integers
> > > are the some size.  For every integer, you can name a corresponding
> > > even integer (2 X the integer).  Since this is a one-to-one and onto
> > > relationship,  the two infinities are equal.  Isn't god wonderful???
> > >
> > > Charlie
> >
> > In another response to this thread, I wrote:
> >
> > "It has something to do with both of them being "countably infinite",
> > since you can make direct correspondences between members of each set,
> > i.e.  1 with 1 AND -1, 2 with 2 AND -2,...ad infinitum."
> >
> > OKAY, MATH GEEKS:  Who's right, (if anyone) and why?
> >
> 
>         You both are.  Fundamentally you're doing the same thing, but in a
> different way.  You're describing all integers (negative and positive)
> he's dealling with integers and even integers.  Not a big difference.
> All of them are equally infinite.
> 
> Now the question is, there is as I understand it, at least a 3rd order
> of Infinity.  Does anyone know what it is?
> 

To use Cantor's transfinite notation:

aleph-null is the countable infinity of the integers
aleph-1 is the first uncountable infinity, of the rationals
aleph-2 is the second uncountable, the reals

Further infinities are denoted by additional aleph numbers (aleph, BTW, 
is the first letter of the Hebrew alphabet -- all the Greek letters were 
already in use by Cantor's day).

-- 
A confidence man knows he's lying; that limits his scope.  But a
successful shaman believes what he says -- and belief is contagious;
there is no limit to >his< scope.  -- Jubal Harshaw, M.D, J.D.

Donald Qualls, aka The Silent Observer           NAR # 70141-SR Insured
silent1@ix.netcom.com        http://members.aol.com/silntobsvr/home.htm 
Rocket Pages              http://members.aol.com/silntobsvr/modrocs.htm

Opinions expressed are my own -- take them for what they're worth
and don't expect them to be perfect.