Re: Godel Goofed? Nope.

[olcott <olcott@qwest.net>]

All of this is merely a matter of looking at things
one way or another... We can look at the fact
that Even Roots of Negative Numbers can not
exist, or we can ignore this, and make pretend
that they do exist... What's important to me,
is whether or not Godel Goofed...

Simon Biber wrote:

> 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.
> > > >
> >