Good example! Linda -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Björn Helgason Sent: Tuesday, November 17, 2015 4:32 AM To: Programming forum Subject: Re: [Jprogramming] Why is subtraction and division of rational numbers so hard?
In calendar applications you sometimes set events that are infinite. that is should repeat forever. On 16 Nov 2015 23:51, "Don Kelly" <[email protected]> wrote: > I think that the problem is that infinity is not just a very big > number but is a concept. 0 is a real number but 1%0 is infinite simply > the limit as 1%n as n gets bigger and bigger- a point never reached. > It is not a number as it is beyond all numbers. J recognizes this and handles some > cases such as +~__ and *~__ as the results are infinite by definition. > .0%__ simply follows 0%n =0 = for any n -no matter how large. > %~__ or -~__ as these are always indeterminate-hence NaN When > dealing with your young students, I would suggest tables involving > 1+i.n and avoid infinity. Infinity can be treated as a concept in > 1+its own > right but treating it as just another number leads to problems. > > Don > > > On 11/16/2015 6:30 AM, Linda A Alvord wrote: > >> Don, Can you identify which ones of the twenty five items in the >> pairs don't work? >> >> %/~ 1r3%i.5 >> |NaN error >> | %/~1r3%i.5 >> >> Linda >> >> -----Original Message----- >> From: [email protected] >> [mailto:[email protected]] On Behalf Of Don >> Kelly >> Sent: Monday, November 16, 2015 12:59 AM >> To: [email protected] >> Subject: Re: [Jprogramming] Why is subtraction and division of >> rational numbers so hard? >> >> Could it be that 1r3 % i.1 =(1/3)%0 so the result of the summation is >> infinity + some numbers? >> try >> -/~ 1r3 %1 +i.5 >> >> 0 1r6 2r9 1r4 4r15 >> >> _1r6 0 1r18 1r12 1r10 >> >> _2r9 _1r18 0 1r36 2r45 >> >> _1r4 _1r12 _1r36 0 1r60 >> >> _4r15 _1r10 _2r45 _1r60 0 >> >> >> or >> -/~ 1r3 %1r1000000+i.5 >> >> 0 1000000000000r3000003 2000000000000r6000003 1000000000000r3000001 >> 4000000000000r12000003 >> >> _1000000000000r3000003 0 1000000000000r6000009000003 >> 2000000000000r9000012000003 1000000000000r4000005000001 >> >> _2000000000000r6000003 _1000000000000r6000009000003 0 >> 1000000000000r18000015000003 2000000000000r24000018000003 >> >> _1000000000000r3000001 _2000000000000r9000012000003 >> _1000000000000r18000015000003 0 1000000000000r36000021000003 >> >> _4000000000000r12000003 _1000000000000r4000005000001 >> _2000000000000r24000018000003 _1000000000000r36000021000003 0 >> >> >> Don Kelly >> >> >> On 11/15/2015 1:05 AM, Linda A Alvord wrote: >> >>> How would you explain to a 4th grade student why subtraction and >>> division of fraction is so difficult for J. Here is a dialog I >>> wrote to review all the big ideas students should remember from >>> third grade. Tables show how some verbs like + and times are >>> commutative and * and % are not. If the >>> >> verb >> >>> is commutative you need only "master" a little more than half of the >>> >> table. >> >>> >>> >>> >>> +/~i.5 >>> >>> i. >>> 0 1 2 3 4 >>> >>> 1 2 3 4 5 >>> >>> 2 3 4 5 6 >>> >>> 3 4 5 6 7 >>> >>> 4 5 6 7 8 >>> >>> >>> >>> >>> -/~i.5 >>> >>> >>> 0 _1 _2 _3 _4 >>> >>> 1 0 _1 _2 _3 >>> >>> 2 1 0 _1 _2 >>> >>> 3 2 1 0 _1 >>> >>> 4 3 2 1 0 >>> >>> >>> >>> >>> */~i.5 >>> >>> >>> 0 0 0 0 0 >>> >>> 0 1 2 3 4 >>> >>> 0 2 4 6 8 >>> >>> 0 3 6 9 12 >>> >>> 0 4 8 12 16 >>> >>> >>> >>> >>> %/~i.5 >>> >>> >>> 0 0 0 0 0 >>> >>> _ 1 0.5 0.333333 0.25 >>> >>> _ 2 1 0.666667 0.5 >>> >>> _ 3 1.5 1 0.75 >>> >>> _ 4 2 1.33333 1 >>> >>> >>> >>> >>> 1r3%i.5 >>> >>> >>> _ 1r3 1r6 1r9 1r12 >>> >>> >>> >>> >>> +/~ 1r3%i.5 >>> >>> >>> _ _ _ _ _ >>> >>> _ 2r3 1r2 4r9 5r12 >>> >>> _ 1r2 1r3 5r18 1r4 >>> >>> _ 4r9 5r18 2r9 7r36 >>> >>> _ 5r12 1r4 7r36 1r6 >>> >>> >>> >>> -/~ 1r3%i.5 >>> >>> >>> |NaN error >>> >>> | -/~1r3%i.5 >>> >>> >>> >>> */~ 1r3%i.5 >>> >>> >>> _ _ _ _ _ >>> >>> _ 1r9 1r18 1r27 1r36 >>> >>> _ 1r18 1r36 1r54 1r72 >>> >>> _ 1r27 1r54 1r81 1r108 >>> >>> _ 1r36 1r72 1r108 1r144 >>> >>> >>> >>> >>> %/~ 1r3%i.5 >>> >>> >>> |NaN error >>> >>> | %/~1r3%i.5 >>> >>> >>> >>> >>> t=: 13 :'>:/~i.y' >>> >>> >>> t 5 >>> >>> >>> 1 0 0 0 0 >>> >>> 1 1 0 0 0 >>> >>> 1 1 1 0 0 >>> >>> 1 1 1 1 0 >>> >>> 1 1 1 1 1 >>> >>> >>> >>> >>> (t 5)*+/~i.5 >>> >>> >>> 0 0 0 0 0 >>> >>> 1 2 0 0 0 >>> >>> 2 3 4 0 0 >>> >>> 3 4 5 6 0 >>> >>> 4 5 6 7 8 >>> >>> >>> >>> >>> (t 5)**/~i.5 >>> >>> >>> 0 0 0 0 0 >>> >>> 0 1 0 0 0 >>> >>> 0 2 4 0 0 >>> >>> 0 3 6 9 0 >>> >>> 0 4 8 12 16 >>> >>> >>> >>> >>> (t 5)*+/~ 1r3%i.5 >>> >>> >>> _ 0 0 0 0 >>> >>> _ 2r3 0 0 0 >>> >>> _ 1r2 1r3 0 0 >>> >>> _ 4r9 5r18 2r9 0 >>> >>> _ 5r12 1r4 7r36 1r6 >>> >>> >>> >>> >>> (t 5)**/~ 1r3%i.5 >>> >>> >>> _ 0 0 0 0 >>> >>> _ 1r9 0 0 0 >>> >>> _ 1r18 1r36 0 0 >>> >>> _ 1r27 1r54 1r81 0 >>> >>> _ 1r36 1r72 1r108 1r144 >>> >>> >>> >>> >>> Linda I >>> >>> >>> >>> -------------------------------------------------------------------- >>> -- 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 >> >> > ---------------------------------------------------------------------- > 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
