Le vendredi 29 avril 2011 à 11:53 -0700, Julien Rioux a écrit : > On Apr 29, 2:17 pm, Ronan Lamy <[email protected]> wrote: > > I would argue that the correct results are limit(x - oo, x, oo) == -oo > > and limit(oo - x, x, oo) == oo. > > > > The expression whose limit is taken belongs to the extended real line, > > so we need to consider the topology of the extended real line. Unless > > otherwise specified, limits are always evaluated for values of the > > variable close to, but different from, the "destination". In this case, > > this means arbitrarily large, but finite, reals. For any real x, x - oo > > = -oo, so the function Lambda(x, x - oo) is constant over the reals, but > > discontinuous, undefined actually, at x = +oo. However, the latter > > doesn't matter for the limit, and the result is the constant value, -oo. > > All this is completely parallel to limit(abs(x)/x, x, 0, '+'), for > > instance. > > Take f(x,y)=x-y. By your account lim(lim(f(x,y),y,oo),x,oo) == -oo but > lim(lim(f(x,y),x,oo),y,oo) == oo. This can't be right.
Why can't it be right? Limits that don't commute at a singular point are a common occurrence. For instance: lim(lim(exp(-b/a), b, 0+), a, 0+) == 1 lim(lim(exp(-b/a), a, 0+), b, 0+) == 0 Intuitively, the inner variable goes to infinity first, i.e. much faster than the outer one. -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
