Professor Mückenheim Teaches Calculus

[Jürgen R.]

Page 215: The Exponential Function:

Definition.: exp(x) = Sum_0^inf {x^n / n!} (*)

Theorem: exp(x) = lim_{n->inf} (1 + x/n)^n

Proof: (1 + x/n)^n = 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + ....
which converges to (*) in the limit. qed.

C(n,k) is the binomial coefficient.

Apparently he thinks that the convergence of the k-th
term in his binimial expansion to the k-th term in the series
proves the theorem.

A Fool of Matheology (TM Mückenheim) like Hardy takes
a full page to show that (1 + 1/n)^n converges. What
did Hardy overlook that is obvious to Mückenheim?

[Virgil]

Post by Jürgen R.
Definition.: exp(x) = Sum_0^inf {x^n / n!} (*)
Theorem: exp(x) = lim_{n->inf} (1 + x/n)^n
Proof: (1 + x/n)^n = 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + ....
which converges to (*) in the limit. qed.
C(n,k) is the binomial coefficient.
Apparently he thinks that the convergence of the k-th
term in his binimial expansion to the k-th term in the series
proves the theorem.
A Fool of Matheology (TMRo1 ) like Hardy takes
a full page to show that (1 + 1/n)^n converges. What
did Hardy overlook that is obvious to Mückenheim?

I , and mathematicians are much more interested in what WM overlooked
that Hardy did not overlook!


Note that it is easy enough to check that if
y = Sum_0^inf {x^n / n!} converges uniformly, which it does,
then dy/dx = y
and derive what one needs from that, but even to show than
(1 + x/n)^n = 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + ....
or that 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + ....
converges, much less converges to a function equal to its own
derivative, as n -> oo, is something that cannot be easily proved in a
first course in calculas, and probably should not even be attempted, and
certainly not by someone as inept as WM.
--

[m***@rz.fh-augsburg.de]

Post by Virgil

Post by Jürgen R.
A Fool of Matheology (TMRo1 ) like Hardy

Stop lying or will call in the public prosecutor! I never called Hardy a fool!

takes

Post by Virgil

Post by Jürgen R.
a full page to show that (1 + 1/n)^n converges. What
did Hardy overlook that is obvious to M�ckenheim?

Note that it is easy enough to check that if
y = Sum_0^inf {x^n / n!} converges uniformly, which it does,
then dy/dx = y
and derive what one needs from that, but even to show than
(1 + x/n)^n = 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + ....
or that 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + ....
converges, much less converges to a function equal to its own
derivative, as n -> oo, is something that cannot be easily proved in a
first course in calculas,

It can! Of course not everything can be proved in a first course calculus. And I do not even attempt so. But Juergen Rennenkampff from Munich is a well known liar and libeller. Therefore you should not believe him. I prove what he claims to be not proved on p. 215 of
http://www.amazon.de/Mathematik-f%C3%BCr-die-ersten-Semester/dp/348670821X/ref=sr_1_2?s=books&ie=UTF8&qid=1400566108&sr=1-2&keywords=Mathematik+f%C3%BCr+die+ersten+Semester#reader_348670821X
Euler's sequence is shown to be a minorant of Newton's series and also shown to be not less.
Rennenkampff is obviously too stupid to recognize it. But more probably his hatred has overcome him as always. However, I am no longer willing to spend my time with his nonsense.

Regards, WM

[Jürgen R.]

Post by m***@rz.fh-augsburg.de

Post by Jürgen R.
A Fool of Matheology (TMRo1 ) like Hardy

Stop lying or will call in the public prosecutor! I never called Hardy a fool!

You misunderstood, once again. *I* called Hardy a
"Fool of Matheology (TM WM)", I didn't say *you* did.
I consider the term honorific.

Post by m***@rz.fh-augsburg.de
takes

Post by Jürgen R.
a full page to show that (1 + 1/n)^n converges. What
did Hardy overlook that is obvious to M�ckenheim?

It can! Of course not everything can be proved in a first course calculus.
And I do not even attempt so. But Juergen Rennenkampff from Munich is a well known liar and libeller.
Therefore you should not believe him. I prove what he claims to be not proved on p. 215 of
http://www.amazon.de/Mathematik-f%C3%BCr-die-ersten-Semester/dp/348670821X/ref=sr_1_2?s=books&ie=UTF8&qid=1400566108&sr=1-2&keywords=Mathematik+f%C3%BCr+die+ersten+Semester#reader_348670821X
Euler's sequence is shown to be a minorant of Newton's series and also shown to be not less.
Rennenkampff is obviously too stupid to recognize it. But more probably his hatred has overcome him as always. However, I am no longer willing to spend my time with his nonsense.

It turns out that Mückenheim has corrected the error
between the 2nd and 3rd edition of his bestseller.
And Mückenheim forgot to mention this small
detail. I have the 2nd edition here and neglected to check
the 3rd.

The new proof is correct with a small gap, namely that
monotonicity (which direction?) of (1 + x/n)^n, w.r.t. n,
is taken to be self-evident.

So Mückenheim has actually admitted an error. This event
deserves a celebration. I will start a new thread in order
to spread the news as widely as possible.

[m***@rz.fh-augsburg.de]

Post by Jürgen R.
You misunderstood, once again. *I* called Hardy a
"Fool of Matheology (TM WM)", I didn't say *you* did.

But it could easily be understood this way. I am sure you accepted this risk with pleasure.

Post by Jürgen R.
So Mückenheim has actually admitted an error.

This was no error, since my book contains many unproven theorems. I have simply completed some small points during the course of the many editions. I do not remember which one this was.

Regards, WM

[Jürgen R.]

Post by m***@rz.fh-augsburg.de

Post by Jürgen R.
You misunderstood, once again. *I* called Hardy a
"Fool of Matheology (TM WM)", I didn't say *you* did.

But it could easily be understood this way. I am sure you accepted this risk with pleasure.

Post by Jürgen R.
So Mückenheim has actually admitted an error.

This was no error, since my book contains many unproven theorems. I have simply completed some small points during the course of the many editions. I do not remember which one this was.
Regards, WM

ROFL

You have no shame at all, do you?

[FredJeffries]

Post by m***@rz.fh-augsburg.de

Post by Jürgen R.
You misunderstood, once again. *I* called Hardy a
"Fool of Matheology (TM WM)", I didn't say *you* did.

But it could easily be understood this way.

Hilarious!!

First, our hero, who's "publication" consists entirely of quotes (and misquotes) complains when someone posts an actual page from his book.

Now he, the defense of whose thesis consists entirely of misquotation, taking out of context, misdirection and outright fraud complains when someone posts a sentence which may possibly be misunderstood.

[John Gabriel]

Post by FredJeffries

Post by m***@rz.fh-augsburg.de

Post by Jürgen R.
You misunderstood, once again. *I* called Hardy a
"Fool of Matheology (TM WM)", I didn't say *you* did.

But it could easily be understood this way.

Hilarious!!
First, our hero, who's "publication" consists entirely of quotes (and misquotes) complains when someone posts an actual page from his book.
Now he, the defense of whose thesis consists entirely of misquotation, taking out of context, misdirection and outright fraud complains when someone posts a sentence which may possibly be misunderstood.

Another old fool who keeps attacking WM, but finds his arse on the ground every time.

Well, I suppose no one is as stupid as Virgil, who despite being solidly whipped, still screams out "death to WM!" with every last breath. Chuckle.

[m***@rz.fh-augsburg.de]

Post by Jürgen R.

Post by m***@rz.fh-augsburg.de

Post by Jürgen R.
A Fool of Matheology (TMRo1 ) like Hardy

Stop lying or will call in the public prosecutor! I never called Hardy a fool!

You misunderstood, once again. *I* called Hardy a
"Fool of Matheology (TM WM)", I didn't say *you* did.
I consider the term honorific.

Post by m***@rz.fh-augsburg.de
takes

Post by Jürgen R.
a full page to show that (1 + 1/n)^n converges. What
did Hardy overlook that is obvious to M�ckenheim?

It can! Of course not everything can be proved in a first course calculus.
And I do not even attempt so. But Juergen Rennenkampff from Munich is a well known liar and libeller.
Therefore you should not believe him. I prove what he claims to be not proved on p. 215 of
http://www.amazon.de/Mathematik-f%C3%BCr-die-ersten-Semester/dp/348670821X/ref=sr_1_2?s=books&ie=UTF8&qid=1400566108&sr=1-2&keywords=Mathematik+f%C3%BCr+die+ersten+Semester#reader_348670821X
Euler's sequence is shown to be a minorant of Newton's series and also shown to be not less.
Rennenkampff is obviously too stupid to recognize it. But more probably his hatred has overcome him as always. However, I am no longer willing to spend my time with his nonsense.

It turns out that Mückenheim has corrected the error
between the 2nd and 3rd edition of his bestseller.
And Mückenheim forgot to mention this small
detail. I have the 2nd edition here and neglected to check
the 3rd.
The new proof is correct

In fact?

Post by Jürgen R.
with a small gap,

I suspected something like that.

Post by Jürgen R.
namely that
monotonicity (which direction?) of (1 + x/n)^n, w.r.t. n,

Should it begin to oscillate somewhere?

Post by Jürgen R.
is taken to be self-evident.

If you read a bit more carefully you will even find monotony mentioned. Nevertheless I need not a whole page like Hardy did - according to your report which however deserves to be mistrusted in general. But you missed a much larger gap which I have not mentioned, namely 1 + 1 > 1 is assumed to be self evident. According to you and Dan Christensen this is a serious gap. But I will not fill this gap - even in the 100th edition.
Regards, WM

[Virgil]

Post by m***@rz.fh-augsburg.de

Post by Virgil

Post by Jürgen R.
A Fool of Matheology (TMRo1 ) like Hardy

Stop lying

You first!

Post by m***@rz.fh-augsburg.de

Post by Virgil
Note that it is easy enough to check that if
y = Sum_0^inf {x^n / n!} converges uniformly, which it does,
then dy/dx = y
and derive what one needs from that, but even to show than
(1 + x/n)^n = 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + ....
or that 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + ....
converges, much less converges to a function equal to its own
derivative, as n -> oo, is something that cannot be easily proved in a
first course in calculas,

It can!

Not eastly, and WM did not do so.

Post by m***@rz.fh-augsburg.de
Of course not everything can be proved in a first course calculus.
And I do not even attempt so.

But you claim to have done proofs so wituot having done them.
--

[John Gabriel]

Post by Jürgen R.
Definition.: exp(x) = Sum_0^inf {x^n / n!} (*)
Theorem: exp(x) = lim_{n->inf} (1 + x/n)^n
Proof: (1 + x/n)^n = 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + ....
which converges to (*) in the limit. qed.
C(n,k) is the binomial coefficient.
Apparently he thinks that the convergence of the k-th
term in his binimial expansion to the k-th term in the series
proves the theorem.

He thinks very correctly. If it converges to the kth term, it is easily shown by mathematical induction that it converges to any desired term. Q.E.D

In fact, I call it a beautiful and simple proof. 100% rigorous.

Do you feel like an ass? You should. Come to think of it, you are arguing with someone whose thinking ability is on a far higher level than yours could ever be.

While on the topic of sets in other similar threads by Jurgen, it's easy to see that Jurgen cannot understand when two sets are equal.


<more Jurgen crap>

[Jürgen R.]

Post by John Gabriel

Post by Jürgen R.
Definition.: exp(x) = Sum_0^inf {x^n / n!} (*)
Theorem: exp(x) = lim_{n->inf} (1 + x/n)^n
Proof: (1 + x/n)^n = 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + .....
which converges to (*) in the limit. qed.
C(n,k) is the binomial coefficient.
Apparently he thinks that the convergence of the k-th
term in his binomial expansion to the k-th term in the series
proves the theorem.

He thinks very correctly. If it converges to the kth term, it is easily shown by mathematical induction that it converges to any desired term. Q.E.D
In fact, I call it a beautiful and simple proof. 100% rigorous.

If you are trying to crawl still farther up Mueckenheim's
colon it is very bad strategy to rehash his documented errors.

This particular mistake was actually corrected between the
2nd and 3rd "edition" of Muecke's bestseller. Of course,
Muecke is, due to his narcissistic personality disorder,
unable to acknowledge this fact.

In an attempt to further your education: It is in general
incorrect to equate lim_m Sum_n x_nm and Sum_n Lim_m x_nm.
The non-commutativity of mathematical operators seems to be
a major stumbling block for amateurs like you and Muecke.

[John Gabriel]

Post by Jürgen R.

Post by John Gabriel

Post by Jürgen R.
Definition.: exp(x) = Sum_0^inf {x^n / n!} (*)
Theorem: exp(x) = lim_{n->inf} (1 + x/n)^n
Proof: (1 + x/n)^n = 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + .....
which converges to (*) in the limit. qed.
C(n,k) is the binomial coefficient.
Apparently he thinks that the convergence of the k-th
term in his binomial expansion to the k-th term in the series
proves the theorem.

He thinks very correctly. If it converges to the kth term, it is easily shown by mathematical induction that it converges to any desired term. Q.E.D
In fact, I call it a beautiful and simple proof. 100% rigorous.

If you are trying to crawl still farther up Mueckenheim's
colon it is very bad strategy to rehash his documented errors.

The only documented errors I have seen are yours. Chuckle.

Post by Jürgen R.
This particular mistake was actually corrected between the
2nd and 3rd "edition" of Muecke's bestseller. Of course,
Muecke is, due to his narcissistic personality disorder,
unable to acknowledge this fact.

Meh. You've lied so many times and you forget that I am able to read WM's work.

Post by Jürgen R.
In an attempt to further your education: It is in general

This is not a 'general' case, but you missed that as usual. Chuckle.

Post by Jürgen R.
incorrect to equate lim_m Sum_n x_nm and Sum_n Lim_m x_nm.
The non-commutativity of mathematical operators seems to be
a major stumbling block for amateurs like you and Muecke.

That's not what he is saying. But there's the difference between you and WM. You are a mythmatician.

[John Gabriel]

Post by John Gabriel

Post by Jürgen R.

Post by John Gabriel

Post by Jürgen R.
Definition.: exp(x) = Sum_0^inf {x^n / n!} (*)
Theorem: exp(x) = lim_{n->inf} (1 + x/n)^n
Proof: (1 + x/n)^n = 1 + C(n,1)(x/n) + C(n,2)(x/n)^2 + C(n,3)(x/n)^3 + .....
which converges to (*) in the limit. qed.
C(n,k) is the binomial coefficient.
Apparently he thinks that the convergence of the k-th
term in his binomial expansion to the k-th term in the series
proves the theorem.

He thinks very correctly. If it converges to the kth term, it is easily shown by mathematical induction that it converges to any desired term. Q.E.D
In fact, I call it a beautiful and simple proof. 100% rigorous.

If you are trying to crawl still farther up Mueckenheim's
colon it is very bad strategy to rehash his documented errors.

The only documented errors I have seen are yours. Chuckle.

Post by Jürgen R.
This particular mistake was actually corrected between the
2nd and 3rd "edition" of Muecke's bestseller. Of course,
Muecke is, due to his narcissistic personality disorder,
unable to acknowledge this fact.

Meh. You've lied so many times and you forget that I am able to read WM's work.

Post by Jürgen R.
In an attempt to further your education: It is in general

This is not a 'general' case, but you missed that as usual. Chuckle.

Post by Jürgen R.
incorrect to equate lim_m Sum_n x_nm and Sum_n Lim_m x_nm.
The non-commutativity of mathematical operators seems to be
a major stumbling block for amateurs like you and Muecke.

That's not what he is saying. But there's the difference between you and WM. You are a mythmatician.

This comment is being refreshed (oops, rehashed) to embarrass Jürgen R. Chuckle.

Slightly trollish behaviour, but you can't blame me given the fact that I am surrounded by morons.

[Dan Christensen]

This comment is being refreshed....

Refresh this, Troll Boy. (Note recent additions.)


More of John Gabriel's bizarre rantings (all quotes from his postings here at sci.math):

"Hitler was a genius and a very talented artist... As from a moral point of view, again his actions can't be judged, because his morals are different."
-- March 18, 2015


"I will point out a few facts about Hitler that most of you arrogant idiots didn't know or refused to acknowledge because your Jewish overlords do not allow you...

"Unfortunately, Hitler's henchmen got the wrong Jews...


*** NEW *** [Asked if they should have gotten Jews like Albert Einstein, JG has refused to comment.]


"It would be a very good idea to round up all the academic idiots, gas them and incinerate the useless lot. Only those that pass John Gabriel's exam should be allowed to live."
-- July 13, 2014


"Unless I think it's logic, it's not... There are no rules in mathematics... As I have repeatedly stated, if there were to be rules, I'd be making the rules."
-- March 17, 2015


"No stupids. 1/3 does NOT mean 1 divided by 3 and never has meant that"
-- February 8, 2015


*** NEW *** "There is no such thing as a continuous real number line."
-- March 24, 2015


"Indeed, there is no such thing as an instantaneous speed - certainly not with respect to the calculus."
-- March 17, 2015


In John Gabriel's Wacky New Calculus, he cannot even prove that 2+2 = 4.


Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

[John Gabriel]

Post by Dan Christensen

This comment is being refreshed....

Refresh this, Troll Boy. (Note recent additions.)
"Hitler was a genius and a very talented artist... As from a moral point of view, again his actions can't be judged, because his morals are different."
-- March 18, 2015
"I will point out a few facts about Hitler that most of you arrogant idiots didn't know or refused to acknowledge because your Jewish overlords do not allow you...
"Unfortunately, Hitler's henchmen got the wrong Jews...
*** NEW *** [Asked if they should have gotten Jews like Albert Einstein, JG has refused to comment.]
"It would be a very good idea to round up all the academic idiots, gas them and incinerate the useless lot. Only those that pass John Gabriel's exam should be allowed to live."
-- July 13, 2014
"Unless I think it's logic, it's not... There are no rules in mathematics... As I have repeatedly stated, if there were to be rules, I'd be making the rules."
-- March 17, 2015
"No stupids. 1/3 does NOT mean 1 divided by 3 and never has meant that"
-- February 8, 2015
*** NEW *** "There is no such thing as a continuous real number line."
-- March 24, 2015
"Indeed, there is no such thing as an instantaneous speed - certainly not with respect to the calculus."
-- March 17, 2015

1. Lie:

"I abolished 'if and only if' definitions because they are stupid!"

2. Misrepresentation:

"Claiming that 1 divided by 4 is 0.25 is utter rubbish."

It is utter rubbish in the context of the obelus (p -:- q = p/q) where nothing is happening.

3. Lie:

"Gabrielean Axioms of Arithmetic" released -- No more proof by induction!

4. Lie:

He rejects the basic rules of logic.

5. Lie:

He cannot prove something as simple as 2+2 = 4

6. True:

He claims 0.9999... is not equal to 1.

7. Misrepresentation and lie:

He claims 1 divided by 3 is not equal to 1/3.

1 cannot be divided by 3 algebraically and the obelus is a NOP (no operation), that is, 1 -:- 3 =/= 1/3 as ignorantly assumed. While it is possible to divide any unit into any number of parts geometrically, it's not possible to do this algebraically.

8. Misrepresentation and lie:

There are no irrational numbers, so the distance between (0, 0) and (1, 1), for example, is undefined.

I have proved there are no irrational numbers here:

http://www.spacetimeandtheuniverse.com/math/4507-0-999-equal-one-317.html#post21409


9. Misrepresentation, out of context and lie:

There is no such thing as instantaneous speed. (As such, he doesn't know what to make of speedometers on cars that actually show your instantaneous speed. Another "Jewish conspiracy," JG?)

Indeed, there is no such thing as an instantaneous speed - certainly not with respect to the calculus. It is a fallacy that was propagated by Gilbert Strang (MIT). You can mail the idiot here ***@math.mit.edu

Ask him how a car device finds the instantaneous speed.

10. Misrepresentation and out of context:

A linear function has no derivative.

Of course a linear function has no derivative if it is not a tangent line. Only tangent lines have slopes that are called derivatives.

I made the foolish mistake of engaging the moron troll with respect to Peano's spaghetti axioms. No amount of reason can change the ideas of a troll whose brain resides in his arse. I refuse to answer or engage the troll. It is a futile process which results in frustration and unnecessary annoyance.

I shall update this comment, addressing only those false claims that constantly get posted on this newsgroup by the libeler Dan Christensen. While I could sue for harassment, the stress would not be worth the satisfaction of seeing this vile pig end up behind bars where it belongs.

As of today, troll DC has made hundreds of comments repeating the same old lies and vitriol over and over again. This thread will be refreshed every time he continues these actions. There will be no response, because I refuse to discuss mathematics with an irrational psychopath.

Comments are NOT welcome and may not receive any response. This comment is provided in the interests of public education; and to eradicate ignorance and stupidity from mainstream mythmatics.

[Dan Christensen]

Post by Dan Christensen

This comment is being refreshed....

Refresh this, Troll Boy. (Note recent additions.)
"Hitler was a genius and a very talented artist... As from a moral point of view, again his actions can't be judged, because his morals are different."
-- March 18, 2015

No comment, Troll Boy? That was priceless!

Post by Dan Christensen
"I will point out a few facts about Hitler that most of you arrogant idiots didn't know or refused to acknowledge because your Jewish overlords do not allow you...
"Unfortunately, Hitler's henchmen got the wrong Jews...
*** NEW *** [Asked if they should have gotten Jews like Albert Einstein, JG has refused to comment.]

STILL No comment, Troll Boy?

Post by Dan Christensen
"It would be a very good idea to round up all the academic idiots, gas them and incinerate the useless lot. Only those that pass John Gabriel's exam should be allowed to live."
-- July 13, 2014

Charming fellow.

Post by Dan Christensen
"Unless I think it's logic, it's not... There are no rules in mathematics... As I have repeatedly stated, if there were to be rules, I'd be making the rules."
-- March 17, 2015

A classic!

Post by Dan Christensen
"No stupids. 1/3 does NOT mean 1 divided by 3 and never has meant that"
-- February 8, 2015

You really are dumb, aren't you, Troll Boy?

Post by Dan Christensen
*** NEW *** "There is no such thing as a continuous real number line."
-- March 24, 2015

Just plain dumb.

Post by Dan Christensen
"Indeed, there is no such thing as an instantaneous speed - certainly not with respect to the calculus."
-- March 17, 2015

Dumb and dumber.

You are in way over your head here, Troll Boy. Stick to your TeenSpaceCadet forum. You just might be able fool someone there. You are getting nowhere here.

BTW, we are STILL waiting for your proof of 2+2 = 4. What seems to be the problem?

Dan