Didn't you swap 'cardinal' and 'ordinal' below? I think that 'first' and 'second' are ordinal numbers while 'zero', 'one' and 'two' are cardinal numbers.
Ordinal numbers identify items, while cardinal numbers identify in-betweens by counting sets of items. This century is century no 21. The first year of this century is year no 2001, and the last year of this century is year no 2100. Many people celebrated the new century when year 1999 turned into year 2000 - one year too early! Embarrassing! When this century started, 2000 years had passed. When this century ends, 2100 years have passed. Arithmetic is done on cardinal numbers, not on ordinal numbers. That is why i.3 is 0 1 2, I suppose. A very useful arithmetic can be defined on ordinal fractions, but that is a different story. - Bo >________________________________ > Fra: Raul Miller <rauldmil...@gmail.com> >Til: Programming forum <programming@jsoftware.com> >Sendt: 17:15 søndag den 18. december 2011 >Emne: Re: [Jprogramming] J Midterm exam 2011 > >Personally, I like the convention: > >decimal : ordinal : cardinal >0 : zero : first >1 : one : second >2 : two : third >... > >And while this is not the only convention that can be used, I think >it's probably also important to emphasize that people do use different >conventions at times. > >Another classic case where these sorts of distinctions can be >important is "clock arithmetic". > >-- >Raul > > >On Sat, Dec 17, 2011 at 4:00 PM, Dan T. Abell <dab...@txcorp.com> wrote: >> Yes, you're quite right about that. Which would explain >> why I scrapped my initial (zeroth?) answer for one that >> tried to coney a sense of delight in Henry's notation >> as a tool of communication (as opposed to being perfectly >> accurate). >> >> Cheers, >> -Dan >> >> On 17 Dec 2011, at 13:50, Bo Jacoby wrote: >> >>> That does not make the first problem 'problem 0'. Henry's problems are >>> items, not in-betweens. >>> >>> >>> >>> >>>> ________________________________ >>>> Fra: Dan T. Abell <dab...@txcorp.com> >>>> Til: Programming forum <programming@jsoftware.com> >>>> Sendt: 21:21 lørdag den 17. december 2011 >>>> Emne: Re: [Jprogramming] J Midterm exam 2011 >>>> >>>> Ahhh, yes. But what a great way to emphasise that we >>>> begin at zero. We begin our first trip about the sun at >>>> age zero. Before the baker add that first donut, the box >>>> contains zero donuts. ... >>>> >>>> We programmers train ourselves (and future programmers) >>>> to count the jumps, use indices to label the in-betweens >>>> (including that pesky leading "in-between" we call '0'), >>>> and then work to catch all our off-by-one errors. >>>> >>>> -Dan >>>> :-P >>>> >>>> On 17 Dec 2011, at 12:54, Bo Jacoby wrote: >>>> >>>>> when kids count they still say: one two three >>>> >>>> -- >>>> Dan T. Abell :: dabell at txcorp dot com :: 303.444.2452 >>>> Tech-X Corp., 5621 Arapahoe Ave, Ste A, Boulder CO 80303 >>>> http://www.txcorp.com :: 303.748.6894/c 303.448.7756/fx >>>> >>>> >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>>> >>>> >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >> >> -- >> Dan T. Abell :: dabell at txcorp dot com :: 303.444.2452 >> Tech-X Corp., 5621 Arapahoe Ave, Ste A, Boulder CO 80303 >> http://www.txcorp.com :: 303.748.6894/c 303.448.7756/fx >> >> >> ---------------------------------------------------------------------- >> 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
