Donna is a mathematician; see https://en.wikipedia.org/wiki/Cardinal_number
and https://en.wikipedia.org/wiki/Ordinal_number for the natural numbers in the context of ordinals and cardinals. On Thu, May 31, 2018 at 2:16 PM, Raul Miller <[email protected]> wrote: > Ah... true... > > But there's at least two different definitions in use for natural > numbers. These correspond to APL's > > []IO <- 0 > > and > > []IO <- 1 > > See also: https://en.wikipedia.org/wiki/Natural_number > > Thanks, > > -- > Raul > > > On Thu, May 31, 2018 at 2:13 PM, Donna Y <[email protected]> wrote: > > 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 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
