Re: to *** T. Winter

*** T. Winter wrote:
In article <429AAF53.9090007@xxxxxxxxxxxxxxxxxxx> Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> writes:
> On 5/29/2005 3:37 AM, *** T. Winter wrote:
> > > What has happened, is that many mathematicians were unlucky with Leibnitz'
> > and Newton's use of infinitesimals, as something you could calculate with.
> > And indeed the basics were founded on pretty shaky ground. Berkeley was
> > one of those that opposed it. With Weierstrass' limit, infinitesimals
> > where removed from mathematics. And it was only in 1966 that Robinson
> > came with his hyperreals that gave a sound basis for the infinitesimals,
> > and at time they were re-introduced.
> > In my understanding, the infinitesimals correspond to the difference
> between rationals and reals. IR* is based on an illusory notion of infinity.

In that case you have a different interpretation of them than either Newton,
Leibnitz and Robinson.  *R is not based on any a priory notion of infinity.

Can *R be constructed in ZFC-without-the-axiom-of-infinity?
To use infinite sets and ZFC, either formal or informal, *is* using a-priori notions and assumptions about infinity. Or am i missing something?

==
Cheers,
Herman Jurjus
.