> > _ %: _ is _ ^ %_ is _ ^ 0 > > > > anything ^0 is 1.
Of course this is naive. But if you step back to _ ^ %_ and look closer list (]^%) 2^0.25*i.100 1 1.15687 1.2777 1.36221 1.41421 1.43949 1.44426 1.43423 1.41421 1.388 1.35843 1.32757 1.29684 1.26717 1.23916 1.21312 1.18921 1.16745 1.1478 1.13016 1.11439 1.10035 1.08789 1.07687 1.06714 1.05857 1.05104 1.04443 1.03863 1.03356 1.02913 1.02527 1.0219 1.01896 1.01641 1.01419 1.01226 1.01059 1.00914 1.00788 1.00679 1.00585 1.00504 1.00434 1.00373 1.00321 1.00276 1.00237 1.00203 1.00174 1.0015 1.00128 1.0011 1.00094 1.00081 1.00069 1.00059 1.00051 1.00043 1.00037 1.00032 1.00027 1.00023 1.0002 1.00017 1.00014 1.00012 1.00011 1.00009 1.00008 1.00007 1.00006 1.00005 1.00004 1.00003 1.00003 1.00003 1.00002 1.00002 1.00002 1.00001 1.00001 1.00001 1.00001 1.00001 1.00001 1.00001 1 1 1 1 1 1 1 1 1 1 1 1 1 load'plot' plot (]^%) 2^0.25*i.100 ] ^ % is %:~ The choice how we approach infinity with two equal sequences (or same sequence used for both arguments) with the goal to reach _ %: _ is related to the notion that infinity is a single point or any two infinite values are always equal. --- Ralph G Selfridge <[EMAIL PROTECTED]> wrote: > There can be many arguments as to what _%:_ should be, just as I have very > good reasons why 0%0 should be 1. For _%:_ it depends on the path out to > ifinity. When going to an essential singularity any value can be found by > taking the proper path (just as the path to 0%0 can get almost any desired > number, for example go to 0 along the path that provides the limit of > (2x)%x). > > The most important thing is to know what happens in J and work from there. > It will not work if limits out to singularities must take only the path > that I, or others, chose. > Ralph S > > On Mon, 25 Feb 2008, Oleg Kobchenko wrote: > > > 3 %: 8 > > 2 > > 8 ^ %3 > > 2 > > > > _ %: _ is _ ^ %_ is _ ^ 0 > > > > anything ^0 is 1. > > > > --- Henry Rich <[EMAIL PROTECTED]> wrote: > > > >> _ %: _ > >> 1 > >> _ %: __ > >> 1 > >> > >> I'm not sure what these should produce, but it seems like > >> log(_) % _ is at work, which should be NaN, methinks. > >> > >> Henry Rich > >> > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > > > > > > > > > ____________________________________________________________________________________ > > Be a better friend, newshound, and > > know-it-all with Yahoo! Mobile. Try it now. > http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ____________________________________________________________________________________ Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
