Agreed.
For example,
a) zero divide zero is an eigenstate summary-bound inverse of multiplication
by zero
b) imaginary numbers came about because of an imperfect inverse (roots)
c) *Negative* numbers may be regarded as an imperfect invrse extension to be
able to invert addition.
d) have you tried to invert abs()? Makes for an interesting thoguht
exercise:
Can the domain of numbers be extended in such a way as to make this a
useful operation,
similar to imaginary/complex numbers?
How about transfinitesimals? Sets? Intervals?
The domain and i/rnage of the object space under consideration,
the functors involved, and the desired applicative domain
(what results make sense for the functor extensions proposed?)
are all important.
On Tue, Sep 30, 2008 at 1:52 PM, Dan Bron <[EMAIL PROTECTED]> wrote:
> Henry wrote:
> > If you pick one possible result, that's pretty arbitrary and
> > not interesting to me.
>
> I wrote:
> > Do you object to %: then? How about | ? And ^. ? ....
>
> John wrote:
> > The problem is that for a general polynomial, there is no obviously
> > useful systematic restriction.
>
> I'll buy that.
>
> What I don't buy is this philosophy that it's better to have no inverse
> than an imperfect inverse. We've had this discussion numerous times. No
> one complains about (e.g.) ;:^:_1 even though ;: is not 1-to-1.
>
> If we restrict the range of p.^:_1 it may not systematic useful, but an
> error is systematically useless. Further, the cost is not so great: the
> change (like all new inverses) is completely backwards compatible.
>
> -Dan
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
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