In any case it has a number system that includes natural numbers as a subset and natural numbers are both cardinal and ordinal.
Donna Y [email protected] > On May 31, 2018, at 1:50 PM, Raul Miller <[email protected]> wrote: > > J has complex numbers, including imaginary numbers, actually. > > Thanks, > > -- > Raul > > > On Thu, May 31, 2018 at 1:42 PM, Donna Y <[email protected]> wrote: >> 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 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
