128,148 reputation
9121250
bio website von-eitzen.de/math/tntrep.xml
location Bonn, Germany
age 49
visits member for 2 years, 5 months
seen 10 mins ago

I did study math and had a knack for it, but I am sooo out of that business now ...


Jan
28
comment Prove that $\mathbb{Z}$ is a closed subset of $\mathbb{R}$
Where do you get stuck exactly?
Jan
27
comment Primitive polynomials: some statements to (dis-)prove
There are different concepts of primitive polynomial. I assume in this context you mean: The polynomial has no non-unit constant factor? This would match ii) specifically, but then I have nbo idea why you keep bringing up irreducbility ...
Jan
27
comment If a power series converges uniformly on $\mathbb{R}$ then it must be to $0$?
First of all, $\sum_{k=0}^\infty a_k0^k$ is $a_0$, not necessarily $0$. Next, your argument doesn't use anything specific about power funcitons, so it would - if valid - generalize to: If a series of smooth functions converges uniformly, then the limit is constant. A counter-example to this generalization is the Fourier series of a triangular sawtooth function, for example. Note specifically that the $>\epsilon$ in the quote you prove holds only for some $x$ (which may depend on $\epsilon$ and $N$ and whatnot)
Jan
27
comment $\lim_{x \to 0} \sin x ^{\sin x} $ to determine.
First of all, note that the expresseion makes little sense for negative (but almost $0$) values of $x$
Jan
26
comment Are $121$ and $400$ the only perfect squares of the form $\sum\limits_{k=0}^{n}p^k$?
$p$ an integer or $p$ a prime?
Jan
26
comment $f : ]0, \infty[\to\mathbb{R}$ Prove that $\lim_{x\to\infty} f(x) = 0$ if $\lim_{x\to\infty} [f(x)+f'(x)] = 0$
@DavidMitra That (or the knowledge thereof) may depend on the literature used. For example, some only encyclopedia requires for $\frac{f(x)}{g(x)}$ that either $\lim f(x)=\lim g(x)=0$ or $\lim|f(x)|=\lim |g(x)|=\infty$ ...
Jan
26
comment $f : ]0, \infty[\to\mathbb{R}$ Prove that $\lim_{x\to\infty} f(x) = 0$ if $\lim_{x\to\infty} [f(x)+f'(x)] = 0$
Problem is: Are we allowed in the first place to apply l'Hopital? Of course $e^x\to \infty$, but $f(x)e^x$ might a priori oscillate between $0$ and $\infty$.
Jan
25
comment Does the dot product angle formula work for $\Bbb{R}^n$?
Actually, this is used as the definition of angle in higher $n$
Jan
25
comment Is there a subset of natural numbers with a special property
What about $A=\mathbb N\setminus\{1\}$?
Jan
24
comment Can somebody explain with one example the concepts: Lemma-Hypothesis-Theorem-Assumption-Proof-Axiom-Thesis-Determination-Definition-Proof
The differenc between lemma, theorem (and many others, such as proposiiton, claim, corollary) is only in the eye of the beholder. - Maybe the same could sometimes be said about hypothesis, assumption, axiom.
Jan
24
comment Let $F$ be a class of sets. Prove that $B - \mathop{\bigcup}_{A\in F} A = \mathop{\bigcap}_{A\in F} (B-A)$
The claim sounds wrong if $F$ is the empty class
Jan
24
comment What computations would advance math knowledge a lot?
How does "just for one day" put any restriction on "capable of computing anything"?
Jan
24
comment Why does $\sqrt{x} / y =\sqrt{x/y/y}$?
One caveat: The eaquality does not hold with negative $y$.
Jan
22
comment Is it an example of bilinear pairing?
@Holmes.Sherlock Yes (cf. my last statement with $c=1$) and Yes
Jan
21
comment Demonstrate that $B$ is a base in the following linear space…
@JohnG. Consider $T^{n-k-1}(a_0x+\ldots+a_{n-1}T^{n-1}(x))$
Jan
21
comment Dedekind Cuts in Construction of the real line
Depending on your definition of real number, the answer to the first question may be "Yes, by definition"
Jan
21
comment Elementary proofs of prime gap theorems?
@barakmanos But the identity between "trivial" and "has simple proof" may not extend to "obvious". For example, everybody$^{\text{TM}}$ considers Jordan's curve theorem obvious until they attempt to find a simple proof.
Jan
20
comment Why is 15 + 15 different from 15 * 2?
@user2722083 It's about time to revisti your last three years worth of code ;)
Jan
20
comment Why is 15 + 15 different from 15 * 2?
@user2722083 Certainly not, check the docs. Actually, I doubt that any programming language with arithmetic expressions exhibits this confusing behaviour.
Jan
20
comment Which can be logically inferred from the given statements?
Since from the given statements you cannot infer that no objects exist that are doctor bot not women etc., case 2 is not relevant to the question.