"Owen Jacobson" <email@example.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. >
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.
> You're free to involve recursive enumerability in your definition if you > like, but be prepared for misunderstandings.
You are addressing your criticism to the wrong person. "Listable" is not (AFAIK) a technical term with a well defined meaning. I provided a meaning. It is other people who want to redefine the term to simply mean "countable". They should use the term "countable" if they mean "countable". My definition of "listable" is not the same as countable. They are different concepts. For example, computable Reals are countable but not listable. Re-defining a term to mean something different is clearly going to cause problems.
> > -o > >  See for example <2010062122134453246-angrybaldguy@gmailcom>. >