Re: A statement on dbdebunk.

"Chris Smith" <cdsmith_at_twu.net> wrote in message news:MPG.1f53871a83c54be79896da_at_news.altopia.net...
> Just popping in.
>
> Erwin <e.smout_at_myonline.be> wrote:
> > > Remember that isomorphism is 1:1 /and
> > > ONTO/. The mapping is not onto.
> >
> > Can you please explain precisely what difference is made by /and ONTO/
> > ??? I don't understand where you're getting at here. What is the
> > difference between mappings that are indeed "onto" and other mappings
> > that are not "onto" ??????
>
> If you're asking what "onto" means in a mapping, it means that every
> member of some set (which I'll call A) occurs in the right-hand side of
> a binary relation. If that's true for some specific set A, then the
> mapping is described as a mapping "onto A". Otherwise, it's merely a
> mapping "into A".

I think made a mistake a few days ago, when I stated that "a projection is a mapping from one space onto another space." I think it should have been "a projection is a mapping from one space into another space." Unless the subspace covered by the projection is itself the space the projection is "onto". As I said in the other comment, I'm in over my head with the mathematics here. Received on Tue Aug 22 2006 - 12:53:48 CEST