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.
> >> ----------------------------------------------------------------------
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> >
> >
> >
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