Here's the step that I can't understand in the Fibonacci series. How is l different from |. ?
($|i.6)-:$|.i.6 1 (|^:(i.6)1 1)-:|.^:(i.6)1 1 1 (([:+/\|)^:(i.6)1 1)-:([:+/\|.)^:(i.6)1 1 0 (([:+/\|)^:(i.6)1 1);([:+/\|.)^:(i.6)1 1 ┌───┬────┐ │1 1│1 1│ │1 2│1 2│ │1 3│2 3│ │1 4│3 5│ │1 5│5 8│ │1 6│8 13│ └───┴────┘ Linda -----Original Message----- From: Programming <[email protected]> On Behalf Of lindaalvord Sent: Monday, December 3, 2018 11:27 PM To: [email protected] Subject: Re: [Jprogramming] Revisisting the Y combinator Sorry, Jose, I didn't look. 55 is the 10th term! Linda Sent from my Verizon, Samsung Galaxy smartphone -------- Original message --------From: Jose Mario Quintana <[email protected]> Date: 12/3/18 8:20 PM (GMT-05:00) To: [email protected] Subject: Re: [Jprogramming] Revisisting the Y combinator Linda, Please check the Rosetta Code page, I did not produce the Fibonacci sequence, I just showed FIB Y 10 55 and almost everybody there agrees (and apparently so did Binet and de Moivre). Raul showed the sequence 0 1 1 2 ... and he was not the only one. Personally, I have no problem at all with that given the context. I hope it helps On Mon, Dec 3, 2018 at 7:30 PM Linda Alvord <[email protected]> wrote: > Jose, If you look up the derivation of the fibonnaci series was > developed you will find 1 1 2 3 5 . . . > > I think it should be left out of an example of the Y form. Or, maybe > it can be modified to come out correctly. > > I do have a way to generate the correcg formula and feel > mathematicians will be more comfortable with that. > > > Linda > > > > -----Original Message----- > From: Programming <[email protected]> On Behalf > Of Jose Mario Quintana > Sent: Monday, December 3, 2018 6:18 PM > To: [email protected] > Subject: Re: [Jprogramming] Revisisting the Y combinator > > Linda, > > The choice to start the Fibonacci sequence at 0 is to conform with > some of the other answers at the Rosetta Code page, > > Y combinator > > https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Frose > ttacode.org%2Fwiki%2FY_combinator&data=02%7C01%7C%7C4673109620904e > 6c73d008d659a0b678%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636794 > 944120539237&sdata=VUhCaXruQBmADyjRuo3MnUsfN9Nt7wtPqv%2F6ky5r9Mw%3 > D&reserved=0 > > Most people start numbering items at 1 and when producing a function > (Fib) for the Fibonacci sequence the correspondence is, > > 1 2 3 4 5 6 7 8 9 10 ... > 1 1 2 3 5 8 13 21 34 55 ... > > Some of us, and J, start numbering items at 0. So we can use the > correspondence, > > 0 1 2 3 4 5 6 7 8 9 10 ... > 0 1 1 2 3 5 8 13 21 34 55 ... > > So, either way, Fib(10) is 55 and we all agree even if we disagree. > > (Apparently, the Fibonacci function can be extended to the complex > plane and beyond using, the so-called, Binet's formula.) > > I hope it helps > > > On Thu, Nov 29, 2018 at 10:40 PM Linda Alvord > <[email protected]> > wrote: > > > Jose, Somehow this surprised me. > > > > Y=: ($:`)(`:6) > > N=: 1 :'(u@:<:@:<: + u@:<:)^:(1 < ])' > > P=: (5!:1)<'N' > > P Y("0) i.11 > > 0 1 1 2 3 5 8 13 21 34 55 > > > > Y > > ($:`)(`:6) > > N > > 1 : '(u@:<:@:<: + u@:<:)^:(1 < ])' > > P > > ┌────────────────────────────────────────────┐ > > │┌─┬────────────────────────────────────────┐│ > > ││:│┌─────┬────────────────────────────────┐││ > > ││ ││┌─┬─┐│┌─┬────────────────────────────┐│││ > > ││ │││0│1│││0│(u@:<:@:<: + u@:<:)^:(1 < ])││││ ││ > >││└─┴─┘│└─┴────────────────────────────┘│││ > > ││ │└─────┴────────────────────────────────┘││ > > │└─┴────────────────────────────────────────┘│ > > └────────────────────────────────────────────┘ > > > > > > Linda > > > > > > > ---------------------------------------------------------------------- > For information about J forums see > https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.j > software.com%2Fforums.htm&data=02%7C01%7C%7C4673109620904e6c73d008 > d659a0b678%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C63679494412053 > 9237&sdata=mku3QsP3o%2BJTzZg9Rg37b7udCh0zip0OEecYrU0uBRE%3D&re > served=0 > ---------------------------------------------------------------------- > For information about J forums see > https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.j > software.com%2Fforums.htm&data=02%7C01%7C%7C4673109620904e6c73d008 > d659a0b678%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C63679494412053 > 9237&sdata=mku3QsP3o%2BJTzZg9Rg37b7udCh0zip0OEecYrU0uBRE%3D&re > served=0 ---------------------------------------------------------------------- For information about J forums see https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C4673109620904e6c73d008d659a0b678%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636794944120539237&sdata=mku3QsP3o%2BJTzZg9Rg37b7udCh0zip0OEecYrU0uBRE%3D&reserved=0 ---------------------------------------------------------------------- For information about J forums see https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C4673109620904e6c73d008d659a0b678%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636794944120539237&sdata=mku3QsP3o%2BJTzZg9Rg37b7udCh0zip0OEecYrU0uBRE%3D&reserved=0 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
