Re: Constructors motion
On Sat, Dec 3, 2011 at 10:01 AM, Nate Hayes <nh@xxxxxxxxxxxxxxxxx> wrote:
> Hi George,
>
> I basically agree with your points, too. Although may I also be so bold as
> to suggest that decorations truly are (or can be) a Level 1 concept, at
> least as far as *decorated intervals* are concerned.
To the extent that Level 1 is concerned witht he mathematical
propertiers of the system, math already has a concept of "undefined",
"error", or "invalid construction". So representing those concepts in
Level 1 is appropriate. Leaving them out is not appropriate.
> Constructors in this
> sense can be viewed as an interval function that simply takes non-interval
> arguments. This means at Level 1 constructors have a natural domain. So
> (Empty,ndf) for invalid construction is the same as returning (Empty,ndf)
> for an operation like f(xx)=1/xx when xx=[0,0] because [0,0] is not in the
> natural domain of f.
>
> In the interest of moving forward and making progress, though, and since
> decorations are still yet to be settled (and controversial), I don't have
> any problem to say that for *bare intervals* an invalid construction simply
> returns Empty. This is what Motion 5 does, for example, which says that for
> bare intervals 1/[0,0] = Empty.
I disagree. Hiding errors or potential errors) is not a venial sin
(in the von Neuman sense). It is a mortal sin.
Lee Winter
NP Engineering
Nashua, New Hampshire
United States of America