Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Matheology � 258
Replies: 53   Last Post: May 11, 2013 10:07 PM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology 258
Posted: May 9, 2013 4:09 AM

On 9 Mai, 02:48, Ralf Bader <ba...@nefkom.net> wrote:
> Virgil wrote:
> > In article
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

>
> >> On 8 Mai, 21:56, Virgil <vir...@ligriv.com> wrote:
> >> > In article

>
> >> > 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.)

>
> What n? The natural numbers? What has the
> behaviour of the function at infinity to do with calculating the derivative
> at a finite point?

You seem to be surprised. It must be long time ago or never, that you
learned calculus and the most trivial examples?

> >> 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?

Consult an introductory text on analysis, for instance my book
http://www.amazon.de/Mathematik-Physik-10-2012-ersten-Semester/dp/348670821X/ref=sr_1_4?s=books&ie=UTF8&qid=1368086437&sr=1-4&keywords=M%C3%BCckenheim

> > But that one sequence gives a limit does not guarantee that that
> > sequence need give the same result as any other sequence.

Therfore I said "for every sequence (x_n) with limit x_0."
>
> 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)

Don't conclude from your state of understanding on that of authors of
best selling text books.
>
> > 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 proves your absolute ingnorance. Appropriately? What would that
be in mathematics? The simplest counter-example is the function f(x) =
|x| at x = 0. And there are other examples, for instance the function
f(x) = 1 for x = 1/n, n in |N, and f(x) = 0 else.

We see: you do not even know the most simplest foundations of trivial
mathematics, butyou try to understand advanced texts and to judge