Come on bird brain John Garbage-iel, you know you are no saint. Only since you can control yourself
today, doesn't mean you can control yourself today. So far there is usually a spamming stream by a moron
and super-idiot bird brain John Gabriel, who denies all kind of stuff such as: - real numbers - limit - infinite series - piecewise functions - etc..
But nevertheless has a new calculoose, which even cannot differentiate f(x)=x=y.
Am Freitag, 10. November 2017 18:08:31 UTC+1 schrieb John Gabriel: > On Friday, 10 November 2017 10:57:49 UTC-5, George Cornelius wrote: > > In article <*-email@example.com>, > > J*hn G*briel <firstname.lastname@example.org> writes: > > > On Friday, 10 November 2017 00:15:46 UTC-5, George Cornelius wrote: > > > > > >> > Somewhere else I wrote 2*e^(-1/x^2)/x^3 = 1. Sorry for > > >> > that error, but in fact it is also: > > >> > > > >> > lim x->0 2*e^(-1/x^2)/x^3 = 0 > > >> > > >> > Which is a nice little limit exercise. > > >> > > >> The exponential function has an "essential singularity" at infinity. > > > > > > There is nothing "essential" in mathematics and "at infinity" is > > > an impossible scenario. We simply say the function is undefined at > > > x=0 and avoid use of words such as singularity which morons like > > > Stephen Hawking have overused. > > > > You have never taken a course in complex analysis, have you? > > > > >> I have long forgotten my complex analysis but was going to guess that > > >> that implied that it grows near infinity faster than any power > > >> of x, and thus x^(-3)/e^(1/x^2) goes to zero as x goes to zero. > > > > > > There is no limit as I have proved. You cannot substitute a non-number > > > that is, -oo into e^x. e^(-oo) is meaningless nonsense. -oo is not a limit. > > > > > >> > > >> But what do I know? L'Hopital is a bit tricky, but using > > > > > > You can't use L'Hopital's property unless it has the form oo/oo > > > or 0/0 which is not case here. Also L'Hopital fails for several > > > functions which do have those forms. > > > > If you don't mind, I was responding to someone else. I don't > > really care about this ongoing discussion in which you claim > > to have overturned all mathematics as we know it. > > > > So let's agree to something. I gave a solution which is within > > the orthodox mathematical views. That is all. To those who > > do not accept such views, my post is of no interest. It is > > undefined in your world. > > > > It's kind of like playing soccer, or futbol, vs. American > > football. Don't like the game because it's not played by > > your favorite set of rules? Change the channel. > > > > Within complex analysis, "at infinity" clearly has a meaning. You > > deny complex analysis. We're on different playing fields. Heckle > > the referees on your playing field but don't come running over to > > mine and telling me that I'm playing some game prevalent in the > > universe you inhabit by the wrong rules. > > > > George > > > > >> the limit of the log of the function gives you a straightforward > > >> solution for x->0+ . For the other side of the limit you want > > >> (-x)^-3/e^(1/x^2) as x->0+, which will be the negative of the > > >> other limit and therefore zero as well. > > See what I mean Mr. Cornelius? Jan Burse produced 3 new turds on my thread since you fed him. Please do not feed the troll - especially in my threads. Thank you in arrear and in advance!