Henry Rich wrote:
> ^ doesn't have an inverse (unless you make some restrictions).
> So, the flaw in your argument was when you said that ^ and ^.
> cancel each other out.
John Randall wrote:
> The problem here is that a function f has an inverse function
> only if f is 1-1.
Thanks, guys. I knew there was a reason I put the word "proof" in quotes :)
Can you now explain why I was taught, in elementary math, to express %:4 as
(+,-)2 instead of just 2 ? If I have to write (%:4) = (+,-)2 why do I
not have to write (^._1) = 0 j. 1p1 * 1 + 2 * i: _ ? Is it because the
former has only 2 elements, but the latter infinitely many?
By the way, I'm pretty sure 0 j. 1p1 * 1 + 2 * i: N (scalar positive integer
N ) is the right expression for generating for the logs of _1 but J doesn't
agree:
10 {. ^. ^ 0 j. 1p1 * 1 + 2 * i: N =: 10
0j_3.14159 0j3.14159 0j_3.14159 0j3.14159 0j_3.14159 0j3.14159
0j3.14159 0j3.14159 0j3.14159 0j3.14159
~. ^. ^ 0 j. 1p1 * 1 + 2 * i: N =: 10
0j_3.14159 0j3.14159
10 {. q=. M #~ 0j1p1 ~: !.(2^_34) ^. ^ 0 j. 1p1 * M =: 1 + 2 * i:
N =: 1000
_1995 _1993 _1989 _1987 _1985 _1981 _1979 _1973 _1971 _1967
25 {. }. +/\^:_1 q
2 4 2 2 4 2 6 2 4 2 2 4 2 6 2 4 2 2 4 2 6 2 4 2 6
Have I got it wrong? What's the right expression? What I am really generating
with my expression? What's with the odd gaps between successive 0j1p1 ? I
don't see the pattern. Or maybe this is just an implementation issue?
-Dan
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