Re: Thieves Philosophy 101

["Kelli Halliburton" <kelli217@crosswinds.not>]

"olcott" <olcott@qwest.net> wrote in message
3A89A36D.6EF8FC2@qwest.net">news:3A89A36D.6EF8FC2@qwest.net...
>
>
> Jeff Blakeney wrote:
>
> > On Mon, 12 Feb 2001 16:18:23 -0600, olcott <olcott@qwest.net> wrote:
> >
> > >Its just that the semantics are so slippery here...
> > >
> > >while(true)    ==   while(true)      ==    Infinity   ==    1/0
> > >  N++;                    N += 10;
> > >
> > >I am impying no such thing, note that these are infinite loops.
> >
> > The first two are not equivalent.  They are similar in that they are
> > both infinite loops but they change at different rates so therefore
> > they cannot be considered equivalent.
> >
>
> So Infinity + 1 < Infinity + 10 ?
>

I'm sorry; did you really want to start talking about aleph one and
comparative infinites?

Infinites have cardinality among themselves based on the terms skipped.
Aleph one is the infinite number defined as the number of positive integers.
There are infinites with cardinalities both greater and smaller than aleph
one. Example: the set of all even positive integers has a cardinality less
than aleph one. The set of all even integers, both positive and negative,
has a cardinality of aleph one + 1 (because zero is introduced).

Basically, in advanced mathematics, all infinites are not created equal.