128,138 reputation
9121250
bio website von-eitzen.de/math/tntrep.xml
location Bonn, Germany
age 49
visits member for 2 years, 5 months
seen 6 hours ago

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


6h
answered Prove that if $f_n \to f$ uniformly on all closed intervals $[c,d] \subset (a,b)$, then $f_ng\to fg$ uniformly on $[a,b]$
22h
answered What is the probability that a random K-bit odd-number is prime?
22h
answered Proving that $\sup f'\left( \left( 0,\infty \right) \right)=0$ under a certain set of conditions.
23h
answered $(\mathcal{P}(\mathbb{N}),\cap)$ - is a group or not?
1d
answered $x^2+3$ has two zeros over ${\Bbb F}_p$ provided that $x^2+x+1\in{\Bbb F}_p[x]$ has two?
1d
answered The equation $x^4+y^4=z^2$ has no integer solution
1d
comment Prove that $\mathbb{Z}$ is a closed subset of $\mathbb{R}$
Where do you get stuck exactly?
1d
revised Prove that $\mathbb{Z}$ is a closed subset of $\mathbb{R}$
edited tags
1d
answered Primitive polynomials: some statements to (dis-)prove
1d
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 ...
1d
answered Showing that if $A_{1},A_{2},…$ are all algebras then the union of all of them is an algebra
1d
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)
2d
answered If a power series converges uniformly on $\mathbb{R}$ then it must be to $0$?
2d
answered $\lim_{x \to 0} \sin x ^{\sin x} $ to determine.
2d
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 $x$
2d
awarded  soft-question
2d
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 $n$