> In article > <email@example.com>, > WM <firstname.lastname@example.org> wrote: > >> On 8 Mai, 21:56, Virgil <vir...@ligriv.com> wrote: >> > In article >> > <15ddac8c-14be-485b-bac7-213b078c1...@k8g2000vbz.googlegroups.com>, >> > >> > ?WM <mueck...@rz.fh-augsburg.de> wrote: >> > > For all n: f(n) = 1 , lim_n-->oo f(n) = 1 >> > > This is required for correctly calculating differential quotients in >> > > analysis. (Just this morning I explained that in class.)
A new piece of idiotic crap. What n? The natural numbers? What has the behaviour of the function at infinity to do with calculating the derivative at a finite point? The appropriate title for the class would be "How to become as stupid as the lecturer already is, and even pay a small tuition for it"
>> > My sympathy for your poor students to be subjected to such >> > incompetence. >> > >> > Curious that that particular limit appears so rarely in calculating >> > differential quotients or in calculus texts. >> > >> > One does not find it referred to at all in such calculus texts as >> > Apostol. >> > -- >> >> If for every sequence (x_n) with limit x_0 the limit of the sequence >> of difference quotients >> (f(x_n) - f(x_0))/(x_n - x_0) exists and is the same in all cases, >> then df/dx is defined at x_0.
What does this have to do with the above? Did the n's mutate into x_n's or what? But why not - it is of congenial stupidity with the Mückenheimian opinion that the variable bound by a quantifier is an abbreviation for a defining condition of the members of the set the variable varies over.
> But that one sequence gives a limit does not guarantee that that > sequence need give the same result as any other sequence.
Mückenheim will understand neither this nor that he need not teach you how derivatives are defined (and even if, he could not, because he obviously does not understand it himself)
> So unless one has some other guarantee of differentiability at the point > in question, finding a supposed derivative or slope by a sequence is not > guaranteed to work right.
If Mückenheim's crap would be correct, then one could do with just one sequence, appropriately chosen, in the definition of differentiability. This because a function can have at most countably many argument values in Mückenheim's wonderland.