Re: A statement on dbdebunk.

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".

If you are, instead, making the point that it doesn't make sense to say that a function is "onto" unless you imply what set it maps onto, then I agree. Every function, of course, is a mapping onto *some* set. I haven't read the first part of this thread of the referenced statement on the dbdebunk web site, so I don't actually know if this is implied by context, or actually missing.

-- 
Chris Smith