There are Natural numbers that can be used for counting (Cardinal) and ordering (Ordinal).
Indexing arrays is an instance of Ordinals. Counting elements in arrays is an instance of Cardinal. J might not have Irrational or Imaginary or Complex numbers but it does have Natural numbers which can be used as Ordinal or Cardinal even if J does not declare that type. There might be Real or Integer or Rational numbers. The natural numbers with 0, correspond to the non-negative integers Donna Y [email protected] > On May 31, 2018, at 1:22 PM, Raul Miller <[email protected]> wrote: > > On Thu, May 31, 2018 at 11:48 AM, Jose Mario Quintana > <[email protected]> wrote: >>> Are you referring to the notation you invented, here? >> >> The notation I invented? > > Oops, I thought you were Bo, for some reason. I don't remember all the > details of the notations he has proposed. But that's my mistake and > not a relevant tangent in this thread, for now at least. > >>> When I try to look up "finite mathematical ordinals" I don't see >>> anything significant with that label. And when I try to parse that >> >> In general, mathematical ordinals and mathematical cardinals are not the >> same. > > They are indeed different abstractions. Howeve, that does not mean > that there's no equivalences between them. > >>> phrase as individual words, I see no contradiction with what I had >>> said. >> >> I do not see one either (often I respond to posts in sequence without >> necessarily having read all the subsequent posts). > > Fair enough. > > Thanks, > > -- > Raul > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
