Re: DRAFT position paper

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Nate Hayes wrote:
> Arnold Neumaier wrote:
> > Nate Hayes wrote:
> > > For those that may be interested, attached is the current draft of 
> > > the position paper John referred to.
> >
> > Nate Hayes wrote:
> >
> > > we propose an
> > > alternative, including by Proposition 1 (Motion 18) to make the
> > distinction
> > > between 1/0 and 1/Empty with decorations D_1 and D_0,
> >
> > But your scheme fails to make a distinction between 1+1/0 and 1+1/Empty,
> > so your decorations for this distinction cannot be relied upon in a
> > longer calculation.
>
> My scheme reports that both 1+1/0 and 1+1/Empty are ill-formed, as it 
> should be:
>
> 1/0 is undefined, and 1+undefined is ill-formed (as is 1/Empty).

Under these circumstances, what's the point of distinguishing between 
undefined and ill-formed?

The functions f(x):=1/x and g(x)=1+1/x are both defined everywhere
except at x=0, so f(0) and g(0) should both be undefined, or both
be ill-formed.

But it doesn't make sense to label f(0) undefined and g(0) ill-formed,
just because your scheme yields this artificial distinction.