> See also: https://en.wikipedia.org/wiki/Natural_number > Notation[edit > <https://en.wikipedia.org/w/index.php?title=Natural_number&action=edit§ion=4>] > > Mathematicians use N or ℕ (an N in blackboard bold > <https://en.wikipedia.org/wiki/Blackboard_bold>) to refer to the set > <https://en.wikipedia.org/wiki/Set_(mathematics)> of all natural numbers. > Older texts have also occasionally employed J as the symbol for this set.
Once I asked Ken about the name of J language and he referred me to the Book of J for some clues: > Biblical scholarship has, by long and minute labor, and with continuing > controversy, established that these books are a redaction of at least four > separate documents (some say more). One of these, usually regarded as the > earliest, was given the label J, > Nobody knows who J, as the author of J has come to be called for short, was, > and many believe there were several J's; He thought I’d be amused to know that J is thought to be a woman. I wonder if he knew the set of Natural numbers were sometimes represented as J. Donna Y [email protected] > On 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
