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 > ---------------------------------------------------------------------- > 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
