> > > and therefore switching term "well-defined" to "invertible" is
> > > justifiable?
> >
> > I don't think so. Assume that the database consists of only R(a,b) and
> Q(R)
> > = SELECT[a=5](R). In that case the addition Add({(5,6)}) is always a
> > well-defined addition but not invertible as you defined it above.
>
> It seems that the difference is how much we want to quantify the
>
> Q( D + deltaD ) = V + deltaV
>
> No quantification (that is D, V, and deltaV are free) -- then we are
> speaking "well-defined".
>
> Definition #0:
>
> Given D and V such that
>
> Q( D ) = V
>
> and some deltaV, Q is called well-defined if there exists deltaD such that
>
> Q( D + deltaD ) = V + deltaV
>
> The alternative term I might prefer is "locally invertible".
Sorry, I overlooked minimality here again. Time to think more...
Received on Thu Sep 11 2003 - 12:00:41 CDT
