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 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
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