Introducing zero as an ordinal number is not helpful. The widespread confusion
is demonstrated by the fact that the millenium was celebrated erroneously by
the end of year1999 rather than correctly by the end of year 2000. On May 25,
1961, President J. F. Kennedy announced the goal of sending an American safely
to the Moon before the end of the decade. The last year of decade 197 is year
1970, but it was erroneously taken to be year 1969.
Thanks. Bo.
Den 18:24 onsdag den 23. maj 2018 skrev Jose Mario Quintana
<[email protected]>:
That is clever! However, if I am interpreting it correctly, the verb - -
~:&* in the context of the hybrid numbering below does not seem to be as
general as - is in the context of the astronomical numbering:
Historical ... 4 BC 3 BC 2 BC 1 BC AD 1 AD 2 AD 3 ...
Hybrid ... _4 _3 _2 _1 1 2 3 ...
Astronomical ... _3 _2 _1 0 1 2 3 ...
The offsets of some years (left argument) relative to a given year, for
instance, 4 BC match:
_3 _2 _1 0 1 2 3 - _3
0 1 2 3 4 5 6
_4 _3 _2 _1 1 2 3 (- - ~:&*) _4
0 1 2 3 4 5 6
Yet, for AD 3 do not:
_3 _2 _1 0 1 2 3 - 3
_6 _5 _4 _3 _2 _1 0
_4 _3 _2 _1 1 2 3 (- - ~:&*) 3
_8 _7 _6 _5 _2 _1 0
I am afraid another complication is required.
On Sun, May 20, 2018 at 8:36 PM, Raul Miller <[email protected]> wrote:
> Of course, you could use an expression such as (- - ~:&*) if you like...
>
> But, yeah, that convention does seem to be slightly... different from
> straight -
>
> Thanks,
>
> --
> Raul
>
>
> On Sun, May 20, 2018 at 5:54 PM, Jose Mario Quintana
> <[email protected]> wrote:
> > Historians refer to specific years, using a well-known event as an
> anchor,
> > naturally as AD 1, AD 2, AD 3, ... and, going backward, as 1 BC, 2 BC, 3
> > BC, ...
> >
> > Dropping the AD and inserting a - (_ in J) instead of BC allows for a
> > simple general consistent rule for calculating the years elapsed between
> > two dates by subtracting the lower date from the higher date; for
> example,
> > the years elapsed between (say, the beginning of) the year _4 and (the
> > beginning of) the year 30 can be calculated by 30 - _4 ...
> >
> > Nevermind, who cares if you are sometimes off by one year because the
> year
> > 0 is missing? Presumably, some people who like to date celestial events
> > precisely :
> >
> > Astronomical year numbering
> > https://en.wikipedia.org/wiki/Astronomical_year_numbering
> >
> > PS. There has been some debate about the exact year when the actual
> > aforementioned event happened: 4 BC, 1 BC, AD 1, ...
> >
> >
> > On Sat, May 19, 2018 at 9:38 AM, 'Bo Jacoby' via Chat <
> [email protected]>
> > wrote:
> >
> >> The terms "ordinal number" and "cardinal number" has advanced
> mathematical
> >> meanings in the theory of infinite sets and transfinite numbers, but the
> >> words also have ancient meanings in grammar. The semantics of a cardinal
> >> number is to count the elements of a finite set, and the semantics of an
> >> ordinal number is to identify a single element. This century is the
> >> twentyfirst century. That is a 1-origin ordinal number. The number of
> whole
> >> centuries that have passed so far is 20. That is a 0-origin cardinal
> >> number. /Bo.
> >>
> >> Den 12:49 lørdag den 19. maj 2018 skrev R.E. Boss <
> >> [email protected]>:
> >>
> >>
> >> > A solution to the problem is to distinguish between the ordinal
> numbers
> >> (first,
> >> > second, and so on) and cardinal numbers (zero, one, and so on). The
> first
> >> > ordinal number is "first", and the first cardinal number is "zero".
> >> Cardinal
> >> > number are for indexing, not for counting. Thanks. Bo.
> >>
> >>
> >> I like that very much, although I read different things in
> >> https://www.wikiwand.com/en/Ordinal_number
> >> "A natural number (which, in this context, includes the number 0) can be
> >> used for two purposes: to describe the size of a set, or to describe the
> >> position of an element in a sequence."
> >> (...)
> >> " Whereas the notion of cardinal number is associated with a set with no
> >> particular structure on it, the ordinals are intimately linked with the
> >> special kind of sets that are called well-ordered (...) "
> >> (...)
> >> " Ordinals may be used to label the elements of any given well-ordered
> set
> >> (the smallest element being labelled 0, the one after that 1, the next
> one
> >> 2, "and so on") and to measure the "length" of the whole set by the
> least
> >> ordinal that is not a label for an element of the set."
> >> See also https://www.wikiwand.com/en/Cardinal_number .
> >>
> >>
> >> R.E. Boss
> >> ----------------------------------------------------------------------
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> >>
> >>
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> >>
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