Are you referring to the notation you invented, here? 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 phrase as individual words, I see no contradiction with what I had said.
Thanks, -- Raul On Thu, May 31, 2018 at 11:26 AM Jose Mario Quintana <[email protected]> wrote: > > > showing that the argument (4) is actually a cardinal number rather > > than an ordinal number. The element (4 { i.7) is not the fourth but > > rather the first after having dropped 4 elements. The element > > > dropped 0 elements. There are no ordinal numbers in J. > > I was referring to the finite mathematical ordinals, which are the same as > the finite mathematical cardinals, which are the same as the natural > numbers (0, 1, 2, ... ); thus, your comments about ordinal numbers do not > apply to them. > > > > On Wed, May 30, 2018 at 9:08 PM, 'Bo Jacoby' via Chat <[email protected]> > wrote: > > > > > The verb ({) can be considered shorthand for ([:{.}.) > > 4 { i.7 > > 4 > > 4 ([:{.}.) i.7 > > 4 > > showing that the argument (4) is actually a cardinal number rather than an > > ordinal number. The element (4 { i.7) is not the fourth but rather the > > first after having dropped 4 elements. The element (0 { i.7) is not the > > "zeroth" but rather the first after having dropped 0 elements. There are no > > ordinal numbers in J. > > > > Den 1:54 torsdag den 31. maj 2018 skrev Jose Mario Quintana < > > [email protected]>: > > > > > > Raul Miller: > > > This dating system dates back to the romans, and pre-dates the invention > > of > > > the zero. > > > > Right, it preceded the invention of the zero in both, the New World, and > > the Old World. > > > > Bo Jacoby: > > > Are you missing the point? The ordinal numbers used for counting > > centuries > > > and years are 1. 2. 3. and so on. No such thing as a zeroth century. > > > > I do not think so. I am aware that there are different perspectives. > > > > There is no "zeroth century" in between the 1st century BC and the 1st > > century AD (also written just as the 1st century). However, zeroth is > > currently regarded as a word in English and, in that sense of the word, the > > zeroth century AD is the 1st century BC and the zeroth century BC is the > > 1st century AD. (It is a mess precisely because there is no "zeroth > > century" in between!) > > > > One of the dates I mentioned, 13.0.0.0.0, is written in the modern notation > > of the Long Count Calendar. This date, which coincided with a winter > > solstice, refers to the day 0 (i.e., the first day in the context of the > > common English language) of a new cycle. > > > > Likewise, the finite mathematical ordinals are 0, 1, 2, ... and J seems to > > follow this scheme; see, for example, > > > > A. Nouns > > http://www.jsoftware.com/help/dictionary/dicta.htm > > > > In particular, as I showed it before in a previous message (see below), the > > verb { selects the items of its right argument in this natural way. > > Although, if one is prepared to go backward, one can also do the following, > > > > _2 _1{ '3rd' ; '2nd' ; '1st' > > ┌───┬───┐ > > │2nd│1st│ > > └───┴───┘ > > _3 { '3rd' ; '2nd' ; '1st' > > ┌───┐ > > │3rd│ > > └───┘ > > > > PS. From my vantage point, a series of messages preceding this one > > illustrates beautifully what happens when you do not start from zero ;) > > > > > > On Wed, May 30, 2018 at 9:10 AM, Raul Miller <[email protected]> > > wrote: > > > > > Right: the year 1941 was in the twentieth century. > > > > > > This dating system dates back to the romans, and pre-dates the invention > > of > > > the zero. > > > > > > Thanks, > > > > > > — > > > Raul > > > > > > On Wednesday, May 30, 2018, 'Bo Jacoby' via Chat <[email protected]> > > > wrote: > > > > > > > Are you missing the point? The ordinal numbers used for counting > > > centuries > > > > and years are 1. 2. 3. and so on. No such thing as a zeroth century. > > > > 0-origin indexing is useful, but the numbers are not ordinal. The > > degree > > > of > > > > a polynomial is the maximum exponent, and the exponents are cardinal > > > > numbers. So "second degree" is bad language for degree 2. > > > > > > > > Den 0:59 onsdag den 30. maj 2018 skrev Jose Mario Quintana < > > > > [email protected]>: > > > > > > > > > > > > This nice day, May 29, 2018, according to some Day Keepers, is > > > 13.0.5.9.5. > > > > That is right, they have been counting days avoiding inevitable > > > complicated > > > > correction rules when trying to synchronize years and days (KISS). > > (Yet, > > > > the date 13.0.0.0.0 corresponded to December 21, 2012.) > > > > > > > > > > > > On Tue, May 29, 2018 at 9:16 AM, Raul Miller <[email protected]> > > > > wrote: > > > > > > > > > Clearly, this year is 10 Prairial CCXXVI > > > > > > > > > > Well, unless you are using the Hebrew calendar - then it’s the year > > > 5778. > > > > > > > > > > Etc... > > > > > > > > > > (Translation: the answer here depends on your religious beliefs) > > > > > > > > > > I hope this helps. > > > > > > > > > > Have a nice day. > > > > > > > > > > Thanks, > > > > > > > > > > — > > > > > Raul > > > > > > > > > > On Tuesday, May 29, 2018, 'Bo Jacoby' via Chat <[email protected]> > > > > wrote: > > > > > > > > > > > Do we agree that this year, AD 2018, is the eighth year of the of > > the > > > > > > second decade of the first century of the third millenium? Or do > > you > > > > > > consider it to be the seventh year of the first decade of the > > zeroth > > > > > > century of the second millenium? The time passed until year 2018 > > are > > > 2 > > > > > > millenia, 0 centuries, 1 decade and 7 years, but those are not > > > ordinal > > > > > > numbers. > > > > > > > > > > > > Den 3:41 tirsdag den 29. maj 2018 skrev Jose Mario Quintana < > > > > > > [email protected]>: > > > > > > > > > > > > > > > > > > Personally, I feel more comfortable with the usual mathematical > > > > > > perspective: 0 is the first ordinal, 1 is the second, etc. > > Moreover, > > > > > from > > > > > > this perspective (as far as I remember), there is no difference > > > between > > > > > > finite cardinal and ordinal numbers. > > > > > > > > > > > > ] A=. 'First' ; 'Second' ; 'Third' ; 'Fourth' ; 'Fifth' > > > > > > ┌─────┬──────┬─────┬──────┬─────┐ > > > > > > │First│Second│Third│Fourth│Fifth│ > > > > > > └─────┴──────┴─────┴──────┴─────┘ > > > > > > 0 { A > > > > > > ┌─────┐ > > > > > > │First│ > > > > > > └─────┘ > > > > > > 1 2 3 4 { A > > > > > > ┌──────┬─────┬──────┬─────┐ > > > > > > │Second│Third│Fourth│Fifth│ > > > > > > └──────┴─────┴──────┴─────┘ > > > > > > > > > > > > > > > > > > On Sat, May 26, 2018 at 12:38 AM, 'Bo Jacoby' via Chat < > > > > > [email protected] > > > > > > > > > > > > > wrote: > > > > > > > > > > > > > Ordinal numbers are not considered in J. The expression 2{y > > should > > > > not > > > > > be > > > > > > > read as "take the second element of y" but as "skip 2 elements > > and > > > > take > > > > > > the > > > > > > > left element of y". > > > > > > > Ordinal Fractions use one-digit ordinal numbers for indexing. > > There > > > > are > > > > > > > but nine one-digit ordinal numbers: 1 2 3 4 5 6 7 8 9, because 0 > > is > > > > not > > > > > > an > > > > > > > ordinal number, and 10 is not a one-digit number. Digit 0 - not > > > being > > > > > an > > > > > > > ordinal number - is available to indicate empty digit positions. > > > > > > > > > > > > > > Example: The roman numeral MMLIII means (M*2)+(L*1)+(I*3) . It > > can > > > be > > > > > > > encoded (arabic style) without delimiting spaces: 2001003 . The > > > > zeroes > > > > > > > in 2001003 mean that terms involving D C X and V are omitted. > > > > Likewise, > > > > > > the > > > > > > > ordinal fraction 2001003 means (M=2)*.(L=1)*.(I=3). The zeroes > > > > > > > in 2001003 mean that conditions involving D C X and V are > > omitted. > > > > > > > Thanks. > > > > > > > Bo. > > > > > > > Den 0:06 lørdag den 26. maj 2018 skrev Jose Mario Quintana < > > > > > > > [email protected]>: > > > > > > > > > > > > > > > > > > > > > Stopwatches and odometers can also be used to label time > > intervals > > > > to > > > > > > > associate them to events occurring in those intervals and keep > > > track > > > > of > > > > > > the > > > > > > > order in which they take place. In fact, conceptual odometers > > > > counting > > > > > > > days have been used at least for two millennia and detecting a > > day > > > > > when a > > > > > > > big cycle ends and the day when the next begins is extremely hard > > > to > > > > > > miss. > > > > > > > > > > > > > > In addition, by starting at 0 when labelling sequential objects > > the > > > > > > offset > > > > > > > from the anchor is immediately evident; for instance, if the > > > buttons > > > > in > > > > > > an > > > > > > > elevator for the floors of the building are labelled: *G (0), 1 > > ,2, > > > > ... > > > > > > and > > > > > > > I pressed 6, to get to the floor where I am then I know that if a > > > > fire > > > > > > > alarm goes off I will go down the stairs 6 floors and I will be > > on > > > > the > > > > > > > ground floor. However, if the fire alarm would go off right now > > in > > > > my > > > > > > > building, ... I would do nothing because there are too many damn > > > > false > > > > > > > alarms! > > > > > > > > > > > > > > In the context of the common English language, there is little > > > doubt > > > > > that > > > > > > > the ordinal numbers are 1st, 2nd, 3rd, 4th, ... However, in > > > another > > > > > > > context (see, https://en.wikipedia.org/wiki/Ordinal_number ) > > they > > > > are > > > > > 0, > > > > > > > 1, > > > > > > > 2, ... (, ω, and so on). > > > > > > > > > > > > > > Personally, I have no problem relating both by saying 0 is the > > 1st > > > > > > ordinal > > > > > > > number, 1 is the 2nd ordinal, 2 is the 3rd ordinal, 3 is the 4th > > > > > ordinal, > > > > > > > etc. > > > > > > > > > > > > > > I understand that there could be instances where starting from 1 > > > > might > > > > > be > > > > > > > more desirable; apparently, that is the case for your Ordinal > > > > Fractions > > > > > > > where the digit 0 is used for a special purpose (although I > > cannot > > > > see > > > > > > the > > > > > > > difficulty in starting from 0 and using, say, _ for the special > > > > > purpose). > > > > > > > > > > > > > > > > > > > > > On Fri, May 25, 2018 at 5:52 PM, Jose Mario Quintana < > > > > > > > [email protected]> wrote: > > > > > > > > > > > > > > > :D > > > > > > > > > > > > > > > > It seems that these people like complications. They are not > > very > > > > > smart > > > > > > > or > > > > > > > > maybe they are... Job security! > > > > > > > > > > > > > > > > > > > > > > > > On Wed, May 23, 2018 at 7:14 PM, David Lambert < > > > > [email protected] > > > > > > > > > > > > > > wrote: > > > > > > > > > > > > > > > >> Our credit union had used employee numbers for account > > numbers. > > > > But > > > > > > ran > > > > > > > >> out of 5 digit numbers. Did they change our accounts to > > 0abcde? > > > > > No! > > > > > > > >> They > > > > > > > >> multiplied 10 leaving us as abcde0. > > > > > > > >> ------------------------------------------------------------ > > > > > > ---------- > > > > > > > ---------------------------------------------------------------------- > > > > 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
