Of course the limit exists from either direction, but I think his point is that it doesn't exist in the normal sense (from any direction). The real definition of a limit says that |x| < δ, i.e., -δ < x < δ, implies |f(x) - L| < ε.
Actually, SymPy computes limits from a single direction (from the right by default). I think there was an issue once to implement limit from both directions (it would basically check '+' and '-' and return the result only if they matched), but I can't find it now. Aaron Meurer On Mar 18, 2011, at 4:04 AM, Alexey U. Gudchenko wrote: > 18.03.2011 12:49, Hector пишет: > > >> Now mathematically, limit x tending to 0, abs(x)/x should not exist. > > Why not? (tendind from the right.) > > Consider definition of limit: > > "the limit of f as x approaches 0 is L if and only if for every real ε > 0 > there exists a real δ > 0 such that 0 < x < δ implies | f(x) − L | < ε" > > Yes, abs(x)/x at point 0 is not well defined, but the limit with this > definition still exists. > > The same with sin(x)/x (but in this case there is question whether this > function analytical or not, abs(x)/x is not). > > > > -- > Alexey U. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sympy@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
