Yes, perhaps it does not need to be said that limits are "better than infinity" while dealing with some of the same issues (we are still avoiding some some trivialities, while edging up on "the right answer").
That said, here's a J perspective on this issue of limits: area=: (1 % 4 * ]) * 3 o. (2 %~ o.1) * 1 - % (*:100)&* @: area 10^i.20 0 1578.44 1591.42 1591.55 1591.55 1591.55 1591.55 1591.55 1591.55 1591.55 1591.55 1591.55 1591.54 1589.63 1579.64 1547.47 882.529 408.281 40.8281 4.08281 Here, given that increasing the number of sides will be increasing the area we have some reason to believe the limit is approximately 1591.55 We'd of course want some independent way of verifying that that answer is valid. In this case, I think we should believe that we are approximating a calculation of the area of a circle where the circumference of the circle is 100. This means that its radius should be 100%2p1 and its area should be 2p1 * *:radius or: 2p1**:100%2p1 1591.55 Or, corresponding to the limit you saw in wolfram's system: %2p1 0.159155 2p1**:%2p1 0.159155 (If the circle has unit circumference the numerical value of its area matches the numerical value of its radius.) FYI, -- Raul On Wed, Feb 27, 2013 at 2:44 PM, Jose Mario Quintana <jose.mario.quint...@gmail.com> wrote: > I asked WolframAlpha the following: limit of ((x/4) tan((pi/2)(1-x))) as > x-> 0 and it replied: 1/(2 Pi) (together with a nice graph). > > > On Wed, Feb 27, 2013 at 10:41 AM, Raul Miller <rauldmil...@gmail.com> wrote: > >> On Wed, Feb 27, 2013 at 7:30 AM, Aai <agroeneveld...@gmail.com> wrote: >> >> (*:100)&* @: area _ >> >> 0 >> >> No, unfortunately J does not interpret the above sentence in that sense. >> > >> > If I'm not wrong then J is right about this one: >> > >> > pi(n-1) pi 0 >> > tg ------- tg ---- >> > 2 n 2 0 >> > lim -------------- = ---------- = ---- = 0 >> > n -> oo 4 n oo oo >> > >> > But the accuracy gives us a much earlier decline to zero, because >> ... >> >> It's usually a mistake to use infinity in calculations - infinity is >> an inconsistent number so you should expect inconsistent results when >> it is used in calculations. (Something related often happens when >> reasoning about division by an unknown sum.) >> >> Infinity is mostly convenient way of indicating neglect and, ideally, >> focussing the conversation elsewhere. >> >> -- >> Raul >> ---------------------------------------------------------------------- >> 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
