In article <4c281047$0$24370$afc38c87@news.optusnet.com.au>, "Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:
> "Owen Jacobson" <angrybaldguy@gmail.com> wrote in message > news:2010062722302771524-angrybaldguy@gmailcom... > > On 2010-06-27 08:24:15 -0400, Peter Webb said: > > > >> AFAIK, "listable" is not a formally defined mathematical term. > > > > This could be because every time someone presents you with a clear, > > concise definition you don't happen to like, you stop replying to them[0]. > > > > As I have said before, AFAIK there is no accepted definition of "listable". > > I provided a definition. Others want to define it differently. > > > > The definitions you've been presented with numerous times *just in this > > thread* are all variations on "a list of elements of some set S is a > > surjective function L from N (the natural numbers) to S." > > > The definitions I have seen are all equivalent to "countable". These are not > good definitions for three reasons. > > Firstly, we already have a perfectly good word which means "there exists a > surjection from N to the set" which everybody knows, and it is "countable". > > Secondly, the definition I proposed for "listable" is far more in accord > with common usage. Just because you can enumerate all items sold in a > supermarket does not neccesarily mean you can form a shopping list; a > shopping list is not just a list every item sold in supermarkets, it is a > specific list of exactly those items you need. > > Thirdly, I already provided a definition of "listable" which is equivalent > to being recursively enumerable. If people try and redefine terms to mean > something different, then there are going to be misunderstandings.
Since we already have "recursively ennumerable" to mean "recursively ennumerable", just as we already have "countable" to mean "countable", there is certainly no more point in having "listable" mean "recursively ennumerable" than in having it mean "countable".
Therefore I shall continue to regard "listable" and "countable" as synonymous.
