Re: infinity

In article <MPG.1db442ef22f2928998a43b@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> stephen@xxxxxxxxxx said:

> > So you are saying that <oo is not a number, and that the value
> > range can be finite, but not equal to a finite number.

> Yes, certainly not equal to any identifiable number

So TOmatics now contians numbers which are not numbers.

No surprise!



> It's equal to the largest finite natural minus 1, which is certainly
> also finite. Yes, I know, that number doesn't exist.

So that the range is a number which does not exist, but somehow still
exists?

TOmatics beats the looking glass world all hollow.



> > So your value ranges are not numbers. That was what I was trying
> > to determine. "<1" is not a number. When you say that the value
> > range is "<1" all you are saying is that all the differences are
> > less than 1. You are not actually identifying a number as the
> > range.
> If min and max are defined, then the range is equal to some number.
> If one or the other is not defined, clearly the range is everything
> up to, but not including, the LUB of the differences. The range of
> (0,1) is arbitrarily close to 1, but not equal to 1.

Thus it is not-a-number.

Diameters have no such not-a-number difficulties for bounded sets. Every
bounded set in a metric space has a number value for its diameter.

And diameters of unbounded sets do not have number values at all.


> > According to your definition. But as I said, according to your
> > definition, a set can have a finite range, but that finite range is
> > not equal to any finite number.

> Correct.

Then it is not a number. So why does TO keep insistsing that what he
admits is not a number is a number? Just one more of the many idocies
of TOmatics.
.