On Fri, Mar 18, 2011 at 3:34 PM, Alexey U. Gudchenko <pr...@goodok.ru>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" > Hi Alexey, When we say - "the limit of f as x *approaches* 0 ", we are allowing x to approach 0 from any side. ( Here are only two ways of approaching to 0 viz '+ve' and '-ve' but its not true always. For function f(x,y) there are infinitely many ways of approaching to (0,0)). So when x approaches from +ve side the value of function will approach to +1 and when it approaches from -ve side the value of function approaches to -1 and you will never be able to find L in your definition. Hope the attachment will make my point clear. > > Yes, abs(x)/x at point 0 is not well defined, but the limit with this > definition still exists. > I agree with u here. Thats the whole point of defining limit in practical world > > The same with sin(x)/x (but in this case there is question whether this > function analytical or not, abs(x)/x is not). > > I actually didn't get what exactly you are trying to convey. Can you please elaborate? > > > -- > 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. > > -- -Regards Hector Whenever you think you can or you can't, in either way you are right. -- 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.
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