Re: Godel Goofed? Nope.

["Simon Biber" <simon@basilisk2.cjb.net>]

Numbers do not have to have a specific value - they do not even have to be
Real. What I quoted is a correct definition of the everyday mathematical
infinity as used in limits. It obviously doesn't talk about transfinite
numbers like aleph-null.

Infinity is the limit of while(true) n++; but infinity is itself not that
process.

Similarly 1/0 itself is undefined and therefore not infinty, but the limit
as x goes to 0 (from above) of 1/x is infinity.

  lim      _1_   =  infinity
x -> 0+   x

(If you take x to 0 from below instead, then the limit is negative
infinity.)

Simon.


"olcott" <olcott@qwest.net> wrote in message
3A8ECB55.56925AB0@qwest.net">news:3A8ECB55.56925AB0@qwest.net...
> Neither is infinity a number, for EXACTLY the same reason...
> Numbers have specifically values, Infinity is ALWAYS more...
> It is the process of more... It is analogous to my infinite loop...
> The termination value of this loop (that does not terminate)
> is infinity...
>
> Simon Biber wrote:
>
> > This is too easy. That loop does not have a termination value.
> >
> > Simon.
> >
> > "olcott" <olcott@qwest.net> wrote in message
> > 3A8EC51B.1875398C@qwest.net">news:3A8EC51B.1875398C@qwest.net...
> > > Okay, then give me the termination value of this loop...
> > >
> > > while(true)
> > >   N++;
> > >
> > > As soon as you give me the correct termination value
> > > of this loop (which NEVER terminates) thenn, I will
> > > agree with you...
> > >
> > > Simon Biber wrote:
> > >
> > > > > Well I guess that I was less than sufficiently precise here...
> > > > > When the |Denominator| becomes smallest, the value becomes
> > > > > largest... So large in fact that it is no longer even a number...
> > > >
> > > > Even if you keep adding to a number, even if you keep squaring a
number,
> > and
> > > > any other increasing operation, the value can never be "no longer
even a
> > > > number"... all sets of numbers including counting, integer, rational
and
> > > > real go on FOREVER.
> > > >
> > > > Infinity is a concept. It has a precise mathematical description:
"An
> > > > unbounded number greater than every Real Number"
> > > >
> > >
> > > This would be incorrect...
> > >
> > > >
> > > > Any process such as you have described cannot ever cease to be a
real
> > > > number, so cannot ever reach "infinity".
> > > >
> > > > Simon.
> > >
>