But, Ralph, 0 * _ is 0 in J, as is 0 * __ . So in J it's OK to say 0 * _. is 0 .
Henry Rich > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Ralph G Selfridge > Sent: Saturday, February 09, 2008 11:44 AM > To: Beta forum > Subject: Re: [Jbeta] Another incompatibility: _ <. _. > > I see _. as indefinite, unknown, etc and multiplying (or > dividing, and > several others)are still indefinite, unknown etc. So trying > to say that > 0*_. must be zero won't hold water ( what is the logical > value for 0*_ or > 0*__?) I can easily claim that _.*x must be indefinite for > all x so that > _.*0 must be indefinite. > > It seems to me that 0=x % _ for all x, but you must add an > exception, is > just as true for _., its still indefinite. > > Trying to extend arithmetic to the Reals (i.e. including > infinities) has to > be careful. > > Ralph S > > > On Fri, 8 Feb 2008, Mark D. Niemiec wrote: > > > Roger Hui <[EMAIL PROTECTED]> wrote: > >> The answer should be _. for the same reason that x+_. > should be _. . > >> That is, for all numeric atoms x, _. should be the answer for > >> > >> x + _. > >> x >. _. > >> x <. _. > >> _. + x > >> _. >. x > >> _. <. x > > > > The rationale behind indefinites is that they represent a value > > which could theoretically take on any number of different values > > in the domain, but we have no idea of determining just which one > > is appropriate. > > > > In some cases, however, arithmetic involving _. CAN produce > > non-indefinite results, when the result is totally independent > > of the value of the indefinite. For example: > > > > 0 = 0 * _. NB. because 0 = 0 * y for all y > > 0 = _. % _ NB. because 0 = x % _ for all x (except > _ and __) > > > > By the same rationale, we should also have: > > > > _ = _ >. _. NB. because _ = _ >. y for all y > > 1 = _ >: _. NB. because 1 = _ >: y for all y > > > > (and similar for corresponding symmetrical and > antisymmetrical cases) > > > > -- Mark D. Niemiec <[EMAIL PROTECTED]> > > > > > > > > > ---------------------------------------------------------------------- > > 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
